Perspectives of Nonlinear Dynamics:

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CUP Archive, Jan 31, 1992 - Mathematics - 652 pages
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The dynamics of physical, chemical, biological or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book and its companion volume, Perspectives of nonlinear dynamics, volume 1, the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. The presentation and style is intended to stimulate the reader's imagination to apply these methods to a host of problems and situations. The text is complemented by copious references, extensive historical and bibliographical notes, exercises and examples, and appendices giving more details of some mathematical ideas. Each chapter includes an extensive section commentary on the exercises and their solution. Graduate students and research workers in physics, applied mathematics, chemistry, biology and engineering will welcome these volumes as the first broad introduction to this important major field of research.
  

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Contents

First order differential systems
1
harmonic lattice in a periodic potential toroidal magnetic Fields twist maps
33
Models based on third order differential systems
125
Mobius band manifolds some interacting flows from neighboring saddle
132
of r contracting and global attracting character
138
discussion of possible relations the KaplanYorke conjecture
217
prediction of the integrability of equalmass Toda lattices the Flaschka
281
solitons and nonsolitons
348
Coupled maps CM and cellular automata CA
427
Understanding complex systems Order organization Endnotemodels
505
Appendixes
529
Bibliography
553
References added at 1991 reprinting
621
A Notations
627
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About the author (1992)

E. ATLEE JACKSON is Professor of Physics, Emeritus, former Director of the Center for Complex System's Research at the University of Illinois at Urbana-Champaign, and a Fellow of the American Physical Society. He has taught and performed research on nonlinear dynamic phenomena for forty years, and is the author of the two-volume Perspectives of Nonlinear Dynamics.

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