Perspectives of Nonlinear Dynamics: Volume 1

Front Cover
CUP Archive, 1989 - Mathematics - 520 pages
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 the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincaré maps and map-dynamics; empirical computational sciences vis-á-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and pattern dynamics; cellular automata.
 

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Contents

In the beginning
1
A potpourri of basic concepts
18
Xk+1 Fxxc k 1 2 XERceR
57
Preview of coming attractions
251
A A brief glossary of mathematical terms and notation
376
B Notes on topology dimensions measures embeddings and homotopy
382
Integral invariants
393
E The digraph method
400
G The PoincaréBendixson theorem and Birkhoffs a and wlimit sets
409
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