This book is devoted to an important branch of the dynamical
systems theory: the study of the fine (fractal) structure of
Poincare recurrences -instants of time when the system almost
repeats its initial state. The authors were able to write an
entirely self-contained text including many insights and examples,
as well as providing complete details of proofs. The only
prerequisites are a basic knowledge of analysis and topology. Thus
this book can serve as a graduate text or self-study guide for
courses in applied mathematics or nonlinear dynamics (in the
natural sciences). Moreover, the book can be used by specialists in
applied nonlinear dynamics following the way in the book. The
authors applied the mathematical theory developed in the book to
two important problems: distribution of Poincare recurrences for
nonpurely chaotic Hamiltonian systems and indication of
synchronization regimes in coupled chaotic individual systems.
* Portions of the book were published in an article that won the
title "month's new hot paper in the field of Mathematics" in May
2004
* Rigorous mathematical theory is combined with important physical
applications
* Presents rules for immediate action to study mathematical models
of real systems
* Contains standard theorems of dynamical systems theory
General
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