Mathematics-Dynamical Systems

Fractal dimensions for Poincare recurrences

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Title (user) : Fractal dimensions for Poincare recurrencesISBN : 9780080462394,9780444521897,0444521895ISSN : 1574-6917DDC : 514.742LCC : QA614.86 .A32 2006GoogleBook ID : b5ALCvn1KwACOpenLibrary ID : OL19429082MEdition : 1st edSeries : Monograph series on nonlinear science and...
Description

Title (user) : Fractal dimensions for Poincare recurrences

ISBN : 9780080462394,9780444521897,0444521895

ISSN : 1574-6917

DDC : 514.742

LCC : QA614.86 .A32 2006

GoogleBook ID : b5ALCvn1KwAC

OpenLibrary ID : OL19429082M

Edition : 1st ed

Series : Monograph series on nonlinear science and complexity 2

Authors (user) : Valentin Afraimovich, Edgardo Ugalde, Jesus Urias

Authors (google) : Valentin Afraimovich,Edgardo Ugalde,Jesus Urias

Publisher : Elsevier

Language : English

Publication Date : 2006

File Format : pdf

Categories : Science


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Description (user) :
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


------------------------------------------

Description (google) :
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

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