1 Datos Personales
2
Cargos Actuales
3 Educación
4
Áreas de interés actuales
4.1
Otras áreas en las que ha participado.
5
Becas y distinciones obtenidas.
6
Tareas de Asesoramiento
7
Organización de Reuniones Científicas
8
Subsidios recibidos
9 Experiencia
profesional.
10 Antecedentes
Docentes.
10.1
Cargos docentes
10.2
Cursos de grado
10.3
Cursos de Postgrado ofrecidos
10.4
Dirección de trabajos y estudios.
11
Publicaciones.
11.1
Libros
11.2
Tesis
11.3
Publicaciones con proceso de referato en revistas
internacionales.
11.4
Trabajos de divulgación
11.5
Publicaciones en Actas de Congresos.
11.6
Trabajos en proceso de publicación, publicados sin referato o sin
publicar.
11.7
Comunicaciones a Congresos
12
Conferencias ofrecidas.
13 Algunos
libros y reviews que reproducen nuestro trabajo
14
Trayectoria de los becarios e investigadores dirigidos o
co-dirigidos.
15 Reviews del libro:
Nonlinear dynamics ...
15.1
Jerry Huke
15.2
Zentrallblatt fur Mathematik (Mathematics Abstracts) No. 867,
1997.
15.3
Nonlinear Science Today, july 1997
15.4
Essen J. Volimer
15.5
Contemporary Physics, Vol.39, No.1 1998
15.6
SIAM Review. Timothy Sawer
16 Otros
conocimientos.
17 Otros datos
personales
Algunas de las materias dictadas
En 2004 dicté por primera vez Física II (Biólogos y geólogos) dando inicio a un acercamiento entre los departamentos involucrados para actualizar estas materias cuyos programas eran (son?) copias del program de física 2 de los aí±os 70. Los cambios que introduje en el programa en uso de la libertad de cátedra se orientan a reemplazar temas de optica por temas de ondas y sus aplicaciones en biología y geología, la parte de termodinámica fue ampliada saliendose del temario básico (ingenieril) de las máquinas térmicas para introducir termodinámica de las mézclas (relevante tanto a biología como a geología) como termodinámica de las reacciones químicas, estas íºltimas esenciales a la biología molecular de nuestros días.
En 2006 se me comisionó el dictado de Física Contemporanea II. La materia no había sido dictada por dos aí±os, y en aí±os anteriores se habían usado materias sustitutas y hasta una peregrinación por tres materias en un cuatrimestre. La materia carecía de programa. En discusiones con la Dra Dibar (CEFIEC) y en consulta con el Dr. Contreras (responsables del curriculum inicial del profesorado en física) fuimos dando forma a la materia, que no está organizada por contenidos (ya que no tiene un contenido específico), sino como un taller de toma de conocimiento de la actualidad en la investigación en física usando como disparador artículos de temas variados aparecidos en Physics Today en los íºltimos aí±os. Desde la física de partículas elementales hasta los problemas éticos de la física actual, pasando por los lasers, los motores brownianos, la turbulencia y la física de maremotos y terremotos, y otros temas.
Licenciatura
Doctorado y post-doctorado
H. G. Solari, M. A. Natiello and G. B. Mindlin. Nonlinear Dynamics. A two way trip from physics to math. Institute of Physics Publishing (IOP), Bristol (England, 1996), 388 páginas. ISBN 0 7503 0379 4 and 0 7503 0380 8, catálogo QC20.7.N6S65
Hernán G. Solari and Mario A. Natiello. Lasers. Fitzroy Dearborn Encyclopedia of Nonlinear Science, Alwyn Scott Editor, New York and London: Routledge, 2004. ISBN 1 57958 385 7
Mario A. Natiello and Hernán G. Solari. Winding numbers. Fitzroy Dearborn Encyclopedia of Nonlinear Science, Alwyn Scott Editor, New York and London: Routledge, 2004. ISBN 1 57958 385 7
M.A. Natiello and H, G. Solari. The User's Approach to Topological Methods in 3-D Dynamical Systems. World Publisher, Singapore, 2007. ISBN-13 978 981 270 380 4
Licenciatura. Fluctuaciones de presión en resalto hidráulico libre y forzado. FCEN-UBA, 1978.
Doctorado. Dinámica variacional en el problema de muchos cuerpos: el tratamiento de las simetrías. FCEN - UBA, 1984.
E. S. Hernández and H. G. Solari. Irreversible Dynamics of Quasispin systems. Physical Review C 25, 2087 (1982).
H. G. Solari and E. S. Hernández. Quasispin dynamics beyond the Bloch sphere: Exact versus Time-dependent Hartree- Fock evolution. Physical Review C 26, 2310, (1982).
E. S. Hernández and H. G. Solari. Kinetic parameters in the nuclear Fermi gas model at finite temperature. Nuclear Physics A 397, 115 (1983).
H. G. Solari and E. S. Hernández. Symmetry conserving variational dynamics: Application to quasispin systems. Physical Review C 28, 2472 (1983).
H. G. Solari and E. S. Hernández. Study of symmetry breaking in the TDHF calculations. Z. Physik A 321, 155 (1985).
H. G. Solari and E. S. Hernández. On the possibility of dynamical symmetry restoration in the Gaussian overlap hypothetis. Physical Review C 32, 462 (1985).
H. G. Solari. Glauber's coherent states and the semiclassical propagator. J. Mathematical Physics 27, 1351 (1986).
D. Jezek, E. S. Hernández and H. G. Solari. Geometry and time scales of selfconsistent orbits in a modified SU(2) model. Physical Review C 34, 462 (1986).
H. G. Solari. Semiclassical treatment of spin systems by means of coherent states. J. Mathematical Physics 28, 1097 (1987).
H. G. Solari, R. Gilmore and M. Vallieres. U(12) Systematic in nuclei. Physical Review C 35, 320 (1987).
H. G. Solari, E. Eschenazi, R. Gilmore and J. Tredicce. Influence of coexisting attractors on the dynamics of a laser system. Optics Communications 64, 49 (1987).
H. G. Solari and R. Gilmore. Relative rotation rates for driven dynamical systems. Physical Review A 37, 3096-3109 (1988).
H. G. Solari and R. Gilmore. The organization of periodic orbits in the Duffing oscillator. Physical Review A 38, 1566 (1988).
E. Eschenazi, H. G. Solari and R. Gilmore. Global organization of basins of attraction in a driven dynamical system. Physical Review A 39, 2609 (1989).
H. G. Solari and R. Gilmore. Reduction of the Maxwell- Bloch equation to a standard form. Optics Communications 71, 85 (1989).
H. G. Solari and R. Gilmore. Dynamics in the transverse section of a CO2 laser. Journal of the Optical Society of America B7, 828 (1990).
N. B. Tufilaro, H. G. Solari, G. B. Mindlin and R. Gilmore. Relative Rotation Rates: Fingerprints for strange attractors. Physical Review A 41, 5717 (1990).
Classification of strange attractors by integers. G. B. Mindlin, X.-J. Hou, H. G. Solari, R. Gilmore and N. B. Tufilaro. Physical Review Letters 64, 2350 (1990).
Symmetry breaking in a laser: the experimental side. C. Green, G. B. Mindlin, E. J. D'Angelo, H. G. Solari and J. R. Tredicce. Phys. Rev. Lett. 65, 3124 (1990).
Am eficient algorithm for fast O(N*ln(N)) box counting. X-J. Hou, R. Gilmore, G. B. Mindlin and H. G. Solari. Physics Letters A 151, 43 (1990).
G. B. Mindlin, H. G. Solari, M. A. Natiello, R. Gilmore and X-J. Hou. Topological analysis of chaotic time series data from the Belousov-Zhabotinskii reaction. Journal of Nonlinear Science 1 147 (1991).
Structure of chaos in the laser with saturable absorber. F. Papoff, A. Fioretti, E. Arimondo, G. B. Mindlin, H. G. Solari and R. Gilmore. Phys. Rev. Letters 68, 1128 (1992).
R. Gilmore, H. G. Solari and S. K. Kim. Algebraic Description of the Quantum Defect. Foundations of Physics, 23, 873 (1993).
B. G. Mindlin, R. López Ruiz, Hernán G. Solari and R. Gilmore. Horseshoe Implications. Phys. Rev. E48, 4297 (1993).
P. T. Boyd, B. G. Mindlin, R. Gilmore and H. G. Solari. Topological Analysis of Chaotic Orbits: Hyperion. Astrophysical Journal 431, 425 (1994).
Remarks on braids and periodic orbits. M. A. Natiello and H. G. Solari. Jour. of Knot Theory and its Ramifications 3, 511-529 (1994).
Laser with injected signal: the perturbation of an invariant circle. H. G. Solari and G. L. Oppo. Optics Communications 111, 173-190 (1994).
G. B. Mindlin and H. G. Solari. Topologically Inequivalent Embeddings, Phys. Rev. E52, 1497 (1995)
H. G. Solari, M. A. Natiello and M. Vázquez. Braids on the Poincaré section: A laser example. Phys. Rev. E. 54, 3185 (1996).
Tori and Klein bottles in four dimensional chaotic flows. B. G. Mindlin and H. G. Solari. Physica D 102, 177 (1997).
H. G. Solari and B. G. Mindlin. Quasicrystals and strong interactions between square modes. Phys. Rev. E 56, 1853 (1997).
M. Zimmermann, M. A. Natiello and H. G. Solari. Sil'nikov-Saddle-node interaction near a codimension 2 bifurcation: Laser with injected signal. Physica D 109 (1997) 293-314.
A. Duarte and H. G. Solari. Modelling the spatio-temporal dynamics of semiconductor lasers. Optics Comm. 144, 99-108 (1997).
A. Duarte and H. G. Solari. The metamorphosis of the monochromatic spectrum in a double-cavity laser as a function of the feedback rate. Phys. Rev. A 58 614-619 (1998).
A. A. Duarte and H. G. Solari. Stability properties of the monochromatic spectrum in a double-cavity laser. Phys. Rev. A60, 2403-2412 (1999).
J. P. Aparicio and H. G. Solari. Sustained oscillations in stochastic systems. Mathematical Biosciences 169, 15-25 (2001).
J. P. Aparicio and H. G. Solari. Population dynamics: a Poissonian approximation and its relation to the Langevin method. Phys. Rev. Lett. 86, 4183-4186 (2001).
Alejandro A. Duarte and Hernán G. Solari. The Slowly Varying Envelop Approximation in the Laser with Optical Feedback. Phys. Rev. A 64 33803, (2001).
M. G. Zimmermann, M. A. Natiello and H. G. Solari. Global bifurcations in a Laser with injected signal: beyond Adler's approximation, Chaos 11, 500-513 (2001).
Pablo F. J. de Leon, Ezequiel V. Albano, R. C. Salvarezza, and H. G. Solari. Interface dynamics for copper electrodeposition: The role of organic additives in the growth mode. Physical Review E 66, 042601 (2002).
H. G. Solari y M. A. Natiello. Stochastic population dynamics: the Poisson approximation. Physical Review E 67 031918 (2003).
Marcos F. Castez, Bárbara Blum, Roberto C. Salvarezza and Hernán G. Solari. Dynamics of solid growth under gravitational field: Influence of the formation of a diffusive layer. Physical Review E 67, 061605 (2003).
J. P. Aparicio, Hernán G Solari and Never Bonino. Competition and coexistence in host-parasite systems: the myxomatosis case. Population Ecology, 46, 71 - 85, (2004).
Marcos F. Castez, Roberto C. Salvarezza Hernán G. Solari. Probing Universality classes in Solid-on-Solid deposition. Phys. Rev. E 70 011606 (2004).
H. G. Solari y M. A. Natiello. Minimal Periodic Orbit Structure of 2-Dimensional Homeomorphisms. Journal of Nonlinear Science, 15(3), 183-222, 2005.
Marcos F. Castez, Mariano H. Fonticelli, Omar Azzaroni, Luis Vázquez, Roberto C. Salvarezza y Hernán G. Solari. Pattern preserving deposition: experimental results and modeling. Applied Physics Letters, 87, 123104, 2005.
J. P. Aparicio, H. G. Solari y N. A. Bonino. Perspectivas Teóricas Sobre la Dinámica de la Mixomatosis con Aplicaciones en Control Biológico. Ecología Austral 16, 15-28 (2006).
M Otero, H. G. Solari and N. Schweigmann. A stochastic population dynamics model for Aedes aegypti: formulation and application to a city with temperate climate. Bulletin of Mathematical Biology, 68, 1945-1974 (2006).
Marcos F. Castez, Roberto C. Salvarezza and Hernán G. Solari. Modeling growth from the vapor and thermal annealing on micro/nano patterned substrates. Physical Review E 73, 011607, 2006.
M. A. Natiello and H. G. Solari. Blowing-up of deterministic fixed points in stochastic population dynamics. Mathematical biosciences 209, 319-335, 2007. (http://dx.doi.org/10.1016/j.mbs.2007.02.002)
M. Otero, H.G. Solari and N Schweigmann. A stochastic spatial dynamical model for Aedes aegypti. Bulletin of Mathematical Biology 70, 1297-1325 (2008).
M. A. Natiello and H. G. Solari. The topological reconstruction of forced oscillators. Chaos, solitons and fractals, accepted 2009.
H. G. Solari. Los límites de lo predecible (o el anagrama de Newton). Ciencia Hoy, Vol. 6 (31), pag. 18 (1995).
R. A. Lopardo y H. G. Solari. Fluctuaciones de presión en la base de resalto libre. Anales del IX Congreso Latinoamericano de Hidráulica, Mérida, Venezuela, June 1980.
Winding numbers and collisions between attractors in a laser system.
J. Tredicce, R. Gilmore, H. G. Solari and E. Eschenazi. In Lecture Notes in Physics 282 ,273 (1987). F. Ehlotzky (Ed.).
Lasers as a test bench for theories of non-equilibrium structures. J. R. Tredicce, E. J. D'Angelo, C. Green, G. B. Mindlin, L. M. Narducci, G. L. Oppo and H. G. Solari. Proceedings of the workshop on Instabilities and nonequilibrium structures, Valparaiso, Chile (1989). E. Tirapegui and W. Zeller eds. Kluner Academic Publishers.
Topological description of dynamical systems. R. Gilmore, G. B. Mindlin and H. G. Solari. In Proceedings of the International Workshop on Quantitative Measures of Dynamical Complexity in Nonlinear Systems. N. B. Abraham, A. M. Albano, A. Passamente and P. E. Rapp Eds. (Plenum, N.Y. 1990).
Symmetry Breaking and Defect Mediated Turbulence in Lasers. J. R. Tredicce, E. J. D'Angelo, C. Green, G. B. Mindlin, L. N. Narducci, H. G. Solari, G. L. Oppo and L. Gil. OSA Proceeding on Nonlinear Dynamics in Optical Systems, V7. Ed. N. B. Abraham, E. M. Garmire and P. Mandel.
Relative Rotation Rates for Driven Dynamical Systems. H. G. Solari and R. Gilmore. In Proceedings of the International Workshop on Quantitative Measures of Dynamical Complexity in Nonlinear Systems. N. B. Abraham, A. M. Albano, A. Passamente and P. E. Rapp Eds. (Plenum, N.Y. 1990).
Comments on the topological organization of periodic orbits. H. G. Solari, M. A. Natiello, G. B. Mindlin and R. Gilmore. Proceedings of the workshop on Instabilities and nonequilibrium structures, Valparaiso, Chile (1991). E. Tirapegui and W. Zeller eds., Kluner Academic Publishers.
H. G. Solari and M. A. Natiello. Poisson approximation to density dependent stochastic processes. A numerical implementation and test. Dynamical Systems from Number Theory to Probability, Vaxjo Univ. Press. Ser. Math. Modelling, 7, 2003.
R. Fernández, H. G. Solari y C. Faerman. Criterios finales para el cálculo de protección radioquímica del proyecto LPR. Reporte Interno CNEA PQ/IPQ 157 (1980).
J. F. Heagy, G. B. Mindlin, H. G. Solari and R. Gilmore. Integrability in Hilbert space: Classical and Quantum Mechanics. Reporte interno, Drexel University, abril de 1989.
H.G. Solari and F. Castez. On Langevin equations for fluctuating surfaces, septiembre de 2006.
M. J. Otero y H. G. Solari. Stochastic eco-epidemiological model of dengue disease transmission by Aedes aegypti mosquito. 2009.
M. L. Fernández, M. J. Otero, N. Schweigmann y H. G. Solari. A mathematically assisted reconstruction of the yellow fever outbreak in Buenos Aires, 1871 (part one): the initial focus. 2009.
An Experimental Approach to Nonlinear Dynamics and Chaos by Nicholas B. Tufillaro, Tyler Abbot, Jeremiah Reilly.
Chaos and Nonlinear Dynamics. Robert C. Hilborn, Oxford University Press, New York. ISBN 0-19-508816-6
Coping with chaos. E. Ott, T. Sawer and Y. York eds. John Wiley and Sons. Reproduces Structure of chaos in the laser with saturable absorber. F. Papoff, A. Fioretti, E. Arimondo, G. B. Mindlin, H. G. Solari and R. Gilmore. Phys. Rev. Letters 68, 1128 (1992).
H D I Abarbanel, R Brown, J J Sidorowich and L Sh Tsimring, The Analysis of Observed Chaotic Data in Physical Systems, Rev. Mod. Phys. 65, 1331, 1993.
Analysis of observed Chaotic Data. Henry Abarbanel. ISBN 0387983724.
W. Ghrist , P.J. Holmes and M.C. Sullivan Knots and Links in Three-Dimensional Flows, 1997. ISBN 3-540-62628-X
R. Gilmore. Topological analysis of chaotic dynamical systems. Review of Modern Physics 70, 1455-1530 (1998).
M. Stone, Kee-Su Park and A. Garg. The semiclassical propagator for spin coherent states. Journal of Mathematical Physics 41, 8025-8049 (2000).
Nota: la numeración de los trabajos se refiere a la lista de trabajos publicados en revistas internacionales con proceso de referato.
Bernardo Gabriel Mindlin. El Dr. Mindlin fue dirigido por Robert Gilmore (PhD) actuando yo como codirector como lo acreditan las publicaciones en comíºn de ese periodo [17-22, 24]. El Dr. Mindlin ha tenido una brillante carrera como profesor primero en la Universidad de Navarra (Espaí±a) y luego en la de Buenos Aires, se ha hecho acreedor a varios premios y es sin duda uno de los mejores investigadores del Departamento de Física de la FCEyN (UBA).
Martín Zimmermann. El Dr. Zimmermann realizó su trabajo de tesis de licenciatura bajo mi dirección. El trabajo realizado se proyectó en su doctorado bajo la dirección del Dr. Mario A. Natiello en la Universidad de Uppsala (ver [34]). El Dr. Zimmermann realizó un postdoctorado en la Universidad de las Islas Baleares para finalmente retornar al Departamento de Física de la FCEyN (UBA) reincorporándose al grupo de trabajo. Sus intereses actuales lo han llevado al estudio de problemas de auto-organización en sistemas socio-económicos habiendo logrado una buena repercusión con estos trabajos (ver Physical Review Focus 6, 28 (2000) [22 December 2000]. Stock Market: Follow the Leader, by David Ehrenstein. http://focus.aps.org/v6/st28.html).
Juan Pablo Aparicio. El Dr. Aparicio decidió reorientar su carrera hacia temas de matemática aplicada a la biología al realizar su doctorado. Finalizado el mismo tuvo la inusual oportunidad de elegir entre varias ofertas de becas postdoctorales optando por el Departamento de Bio-matemática de la Universidad de Cornell, donde trabajó bajo la supervisión del Dr. Castillo Chavez. Obtuvo las becas de postgrado nacional e internacional del CONICET optando por regresar al país para trabajar junto al Dr. Angel Capurro, decisión que se vió frustrada por el fallecimiento del Dr. Capurro. Actualmente se interesa por temas de matemática aplicada al estudio de problemas epidemiológicos, ecológicos y al manejo de recursos naturales.
Alejandro A. Duarte. El Licenciado Alejandro Duarte se doctoró en el Instituo Balseiro en agosto de 2001. Sus intereses personales lo han llevado a empeí±ar su voluntad en temas de economía. En tal sentido renunció a su beca del CONICET aprovechando una oportunidad de incorporarse al grupo de análisis de riesgo y control del CITIBANK. Desde esa posición continuó y completó su trabajo de tesis de doctorado. Finalmente obtuvo una beca de la Fundación Fullbright para realizar un master en temas de economía en la Universidad de Cornell (Agosto-2000). La meta perseguida por el licenciado Duarte es lograr aplicar su formación en el análisis de problemas dinámicos a temas de economía, tanto en el ámbito académico como en el asesoramiento a empresas, habiendo elegido sin duda un largo pero extremadamente serio camino para el logro de sus objetivos.
The rise in popularity of dynamical systems theory, fueled largely by a widespread interest in the phenomenon of chaos, has led to an increasing flood of textbooks on the subject onto the market, and it would appear that any new one would face stiff competition. However, the book under review occupies a niche that is not well supplied; it is a graduate level book, aimed specifically at physicists who want to apply die tools of nonlinear dynamics to their own research problems. As such ¡t sets itself the ambitious targets of not only describing nonlinear dynamics, but of presenting the main mathematical techniques and of showing how these are applied in the investigation of experimental and observational data. Since any one of these in itself could (and currently does) form the subject matter of a book, ¡t is not to be expected that the authors can provide a comprehensive and detailed coverage. What they do provide is a stimulating and challenging book that conveys well the flavour of nonlinear dynamics as an active area in physics, and that hopefully will encourage physicists to acquire the ideas and apply them in a broad range of contexts.
The style of the book is rather different to that of the more well established books at this level, (notably J. Guckenheimer and P. Holmes's "Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields"): the authors go to great lengths to set the theory in the context of physical problems, describing how the problems engender and shape the theories and the associated mathematics. This style of presentation leads them, for example, to introduce homoclinic bifurcations in the context of numerical experiments on the Lorenz system, to follow with a general discussion of global bifurcations in which homoclinic tangles and horseshoes are introduced, and then to give a more detailed discussion of horseshoes and their symbolic dynamics. A more mathematically oriented presentation would probably have taken these subjects in just the reverse order. Other manifestations of the authors' theme of nonlinear dynamics as a tool for physicists are: the inclusion of a chapter on numerical experiments, illustrating how such simulations are an important source of information about models, prompting and guiding the subsequent theoretical analysis; and the inclusion of a chapter on how experimental data can be manipulated to investigate the dynamics of the underlying system, using embedding techniques.
Most of the usual topics in nonlinear dynarnics get an airing: there is a general introductory chapter describing flows, orbits, attractors, Poincaré sections and so on, and there are chapters on stability, local bifurcations, global bifurcations, maps of the interval, and averaging methods. Some less common topics also make an appearance: there is a chapter on the role of symmetry in bifurcations, and one on the topological properties of three dimensional flows.
With this much ground to cover ¡t is inevitable that the authors spread themselves rather thinly at times. The discussion of some of the mathematical tools (such as local Poincaré maps, or Liapunov exponents) is sketchy, and could leave the uninitiated reader unsure about how these things are actually used. Since this book is aimed primarily at physicists and other physical scientists there is very little in the way of formal proof; the more intuitive arguments which are presented instead will appeal to many, but may not be to everyone's taste, especially not those with a more mathematical bent. Part of the answer to this lies in the remark in the Preface that "this is a book to be read with paper and pencil at hand". This is certainly true: the reader is often left to fill in the details for him/herself, and will no doubt get the most out of the book by doing so. But as well as paper and pencil, occasional reference to Guckenheimer and Holmes might be useful to flesh out some of the arguments.
Apart from a willingness to put pencil to paper, the book requires a grounding in elementary topology, (open and closed sets, and homeomorphisms are talked about with little preamble). For some physics graduates this could be a problem, but a standard ancillary analysis course, up to and including metric spaces, would probably provide sufficient background. Some familiarity with ordinary differential equations would be helpful, as would some knowledge of linear systems.
Though ¡t makes fairly serious demands on the reader, the research physicist who works through this book will gain rich rewards in a broad familiarity with nonlinear dynamics and its applications. lt. might even cause them to look at the phenomena they study in a new way.
Jerry Huke, Mathematics Department, University of Manchester Institute of Science and Technology.
email: J. P. Huke @umist.ac.uk.
The authors of this graduate text promise to provide the reader with the mathematical tools of nonlinear dynamics needed to tackle problems in all areas of physics. Topies covered are: introductions to linear and nonlinear dynamics and the elements of their description, elementary stability theory, two- and three-dimensional-flow, local and global bifurcations, horseshoes, and the extraction of qualitative dynamical behavior from recorded data. The initial promise, however, is not kept: this is mainly a descriptive text about nonlinear physics with some additional equations and graphs. In this respect the book succeeds quite well: where other texts are often too brief in their discussion of methods and results, it provides extensive discussion of these topics, which makes it an ideal companion of the standard textbooks. K. Brod (Wiesbaden).
Perhaps surprisingly, given its origins in celestial mechanics, modern nonlinear dynamics has never made it into the core physics curriculum. As the authors of Nonlinear Dynamics: a Two-Way Trip from Physics to Math, observe in the Preface, quantum mechanics, which also has its origins around the turn of the century, caught the attention of the physics community and quantum mechanics deals with linear operators on linear (Hilbert) spaces after all. In some of the more phenmenological areas of physics, however, nonlinear dynamics has found fertil soil: fluid dynamics, plasma physics, mesoscopic physics (quantum chaos), to name a few. The authors of the present book are active in the field of laser dynamics. and it shows.
Reflecting the increasing interest in the application of dynamical systems to virtually every field of researeh, recent years have seen a proliferation of Books pitched at the advanced undergraduate/first-year graduate level. Books presenting the key elements of theory are, for example, Rasband [1], Hale & Koccak [2], Ott [3], Strogatz [4], Glendinning [5] and Verhulst [6]. Besides these general texts there is a good helping of books aimed at specialised audiences of a more pure (e.g., Palis & Takens [7]) or more applied (e.g., Moon [8], Schuster [9]) flavour. The book under review is directed to begining graduate student and reaserchers in physics, mathematics and engineering, but will mostly-appeal to physicists. It is meant to be a comprehensive text. In 16 chapters the 350 pages or so cover a wide range of topics. The somewhat enigmatic subtitle, as explained in the Preface, refers to the hand-in-hand approach of mathematics and physics in the evolution of problems and solutions (i.e., theories) in our sciencific nquires. The pairs classical mechanics-calculus (Newton), quantum mechanics-Hilbert spaces (Von Neumann) and nonlinear dynamics-topology (Poincaré) serve as examples.
The style of the book is informal and people should not be put off by the message on the back cover that "The book presents rigorous results..." A fair selection of key results is presented in the form of theorems but proofs are omitted (or sketched, in rare cases). References to the literature are given instead. The organisation of the material is well thought-out and each chapter ends with a brief summary.
The story begins in Chapter 1 with a description of some experiments illustrating that physical systems can show markedly different behaviour as parameters (physical control variables) are varied. As examples we are offered turbulent fluids, modulated lasers and symmetry-breaking plasmas. In the next six chapters the elementary theory of dynamical systems is presented: linear dynamics, limit sets, invariant manifolds, Poincaré sections, (structural, Lyapunov) stability, two-dimensional flows and bifurcations. By then we have also had a closer look at some mathematical models underlying the phenomena reviewed in Chapter 1. The chapter on two-dimensional flows essentially deals with the Poincaré-Bendixon theorem classifying the possible limit sets of such systems. Some unnecessary confusion is caused by the fact that there are two results presented under the name Poincaré-Bendixson Theorem, one a, lemma to the other.
Chapter 7 on birfurcations first introduces centre manifold reduction and normal forms and then gives a survey of the simple local codimension-one bifurcations. All of this for maps as well as flows. Relatively match time is spent, on discussing the delicated Hopf biftircation for maps (treatment of the stringly resonant cases is deferred till after the introduction of averaging in Chapter 14). This bnifurcation, which also goes under the name of Naimar-Sacker bifurcation, is called a codimension-two bifurcation by the authors, while only its codimension one cases are treated. Indeed, codimension-two bifurcations receive hardly any attention at all in the book.
Chapter 8 presents results of numerical simulations of some low-dimensional continuous and discrete systems focusing on period-doubling cascades, mode-locking, the Lorenz attractor and crisis. Here we have our first encounter with chaotic dynamics, loosely defined in the text as the aperiodic behaviour observed in numerical experiments. Chaos is not popularised in the book. Rather, the authors are interested in the intrincate structure of perriodic orbits underlying complex behaviour and, in the following four chapters, quickly move on to discussing homoclinic tangles, horseshoes, one-dimensional maps, knots and braids. This part of the book is topological/combinatorial in nature. The chapter on the application of the techniques of knots and braids, the authors' own expertise, is one of the best of the book. The subjet is still the domain of a rather specialised group of researchers (many of them working in laser dynamics) and is not found in many other books. The methods of knots and braids can be very powerful in predicting the existence of certain periodic orbits, much like kneading theory does in unimodal maps. Unfortunately, they are in large part restricted to three-dimensional flows with globally defined Poincaré sections, which in practise often means periodically perturbed planar systems.
The final four chapters cover such miscellaneous subjects as experimental time series, Lyapunov exponents, dimensions and entropy, averaging (used to study subharmonic resonance and the strongly resonat Hopf bifurcation). The last chapter on global bifurcations takes up the line of the Chapters 9-12 and treats horseshoe creation in systems with Silnikov-type bifurcations, both with and without symmetry.
My main criticism is that, partly due to the wide spread of material, the discussion tends to remain too superficial for a textbook. This is made worse by the fact that the text contains an insufficient number of examples, which otherwise could have given the book a more explicit character. For instance, there are no examples illustrating the Poincaré-Bendixon and Hopf bifurcation results (either for maps of flows). Instead, the pages are richly sprinkled with exercises, to which parts of the main line of development are relegated. The authors seem to find encouragment for this strategy in a quote by Von Humboldt, but the mathematically inclined or the not so easily convinced might be less quickly reassured. Those will benefit from reading one or two other books simultaneously. On the other hand, the laser models thrpwn in at several places provide useful non-standard illustrations of some interesting dynamical phenomena (subharmonic resonance, Silnikov bifurcation). Despite the book's wide scope, some areas of nonlinear dynamics, inevitably, go uncovered. There is virtually nothing on conservative (Hamiltonian) systems abd (multi)fractals (although Cantor sets are discussed). Nothing will be found on numerical methods (apart from time series analysis), control of chaos, PDEs or inifinite dimensional dynamical systems, pattern formation, complexity or quantum chaos. Since dynamical systems theory is the geometrical approach to differential equations (and iterated maps), figures can be extremely helpful in coveying ideas. In this respect the book is sufficiently illustrated. There is an adecuate list of references.
In conclusion, as someone versed in nonlinear dynamics (and with a background in physics) I enjoyed reading the book, partly because an intuitive account often goes down better than a detailed mathematical exposition. The student, though, might quickly be seen grabbing at mathematically more explicit accompanying material.
Das Buch richtet sich an Naturwissenschaftier und fortgeschrittene Studenten níºt eincm Hinte@nd in der Mathematik oder Physik. Der Leser wird durch die Darstellung von Falibeispicien und eine gro8e Zahl von Obungsaufgaben an die Fragestel]ungen der nichtlinearen Dynamik herapgefí¼hr, und mit wichtigen mathematischen Resultaten und Methoden vertraut gemacht. Dabei ist der Text als Arbeitsbuch gedacht, anhand dessen man sich das Wissen fí¼r eigene Forschung in diesem erarbeiten soll.
Autoren entwickeln die Theorie dynaníºscher ysteme induktiv anhand von physikalischen men. Es werden ausschlieblich Beispiele t dircktem physikalischen Bezug zur Illustrativon Sachverhalten herangezogen und keine
Definitionen ohne eine direktc physikalische Motivation gegeben. Ein grol3er Te¡] der Beispiele bezieht sich auf unterschiedlich getriebene Lasersysteme. Sehr ausfíºhrlich werden die Stabilitát von L¿jsungen und Bifurkationen diskutiert, sowie die topologische Klassifizíerung von niedrigdimensionalen Flí¼ssen und damit asnoziierter Abbildungen. Andererseits sind kiassische Resultate, wie die Kaplan-Yorke-Forrnel fí¼r die fraktale Dimension eines chaotischen Attraktors, nicht erwáhnt.
Fí¼r den erfahrenen Leser ergeben sich durch die an Anwendungen orientarte Darstellung bisweilen interessante Einblicke in Probleme und Einschránkungen be¡ der Anwendung rnathematischer Resultate auf physikalische Probleme. Alierdings findet man nqr schwer Zugang zu dem Buch. Die Darstellung der Theorie leidet, da die Begriffsbildung der Autoren teilweise unklar ist. Einige zentrale Begriffe werden nur indirckt durch den Kontext, in den¡ die Autoren sie verwenden, oder durch Beispiele eingefiihrt.
Wegen dieser didaktischen Schwáchen und der in meinen Augen eigenwilligen Auswahl der Themen wí¼rde ich das Buch als EinfiMng in die nichtlineare Dynan-dk nur bedingt empfehlen. Leser rait erheblicher Erfahrung in dem Gebiet finden jedoch in einigen der weiterfíºhrenden Kapite¡ interessante Anregungen.
J. Volimer, Essen
Another textbook on Nonlinear Dynamics? Some might feel that there are enough already. This book does an excellent job, however, and merits a place alongside the best of those aimed at physicists. Starting from motivating problems in population dynamics, fluid mechanics, laser physics and plasma physics, the authors develop the philosophy, tools and results of dynamical systems theory in a clear and structured way. Unlike some of the purely mathematical texts (e.g. Katok and Hasselblatt), this book gives full weight to the aspects that have been found to be of use in scientific applications. These include centre manifold reduction, bifurcation theory, averaging, Melnikov's method, effects of symmetry and near-symmetry, knots and links in 3D systems, and time series analysis.
On the whole-the book is accurate, but there are a few points where ¡t is weak. The öpen problem" on p.65 about existence of a global Poincaré section was given an answer by Fried in Topology 21 (1982). There are obstructions to smooth linearization not only for saddles (p.77), but also for sinks and sources (see examples in books by Arrowsmith and Place, Wiggins, Glendinning and others). The torsion recursion relationship on p. 142 can be derived from the R* operator of kneading theory. Appeal to the Hartmann-Grobman theorem on p.313 is insufficient for analysis of homoclinic bifurcations: a smooth linearization theorem or at least a smooth normal fórm is required. Nonetheless, I would recommend the book to any physicist (or scientist) who wishes to obtain a grounding in the theory and practice of nonlinear dynamics. It would also make an excellent text for an advanced undergraduate or postgraduate course.
R. S. MACKAY (University of Cambridge)
Picture Omitted
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Cinturón negro de yudo. Campeón argentino en una oportunidad, subcampeón en dos oportunidades.
Profesor superior de Guitarra, conservatorio Santa Cecilia.
Estudioso del comportamiento animal, entrena sus perros de trineo (Malamutes de Alaska).
Practica equitación en forma recreativa (adiestramiento y salto).
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