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<図書>
Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations : fractal dimensions and infinitely many attractors

責任表示 Jacob Palis, Floris Takens
シリーズ Cambridge studies in advanced mathematics ; 35
データ種別 図書
出版者 Cambridge [England] : Cambridge University Press
出版年 1993
本文言語 英語
大きさ x, 234 p. : ill. ; 24 cm
概要 This is a self-contained introduction to the classical theory of homoclinic bifurcation theory, as well as its generalizations and more recent extensions to higher dimensions. It is also intended to s...imulate new developments, relating the theory of fractal dimensions to bifurcations, and concerning homoclinic bifurcations as generators of chaotic dynamics. The book begins with a review chapter giving background material on hyperbolic dynamical systems. The next three chapters give a detailed treatment of a number of examples, Smale's description of the dynamical consequences of transverse homoclinic orbits, and a discussion of the subordinate bifurcations that accompany homoclinic bifurcations, including HTnon-like families. The core of the work is the investigation of the interplay between homoclinic tangencies and non-trivial basic sets. The fractal dimensions of these basic sets turn out to play an important role in determining which class of dynamics is prevalent near a bifurcation. The authors provide a new, more geometric proof of Newhouse's theorem on the co-existence of infinitely many periodic attractors, one of the deepest theorems in chaotic dynamics. 続きを見る

所蔵情報


理系図3F 数理独自 068222194000314 PALI/10/2 1993

理系図 自動書庫 068252193003593 104/PAL 1993

書誌詳細

別書名 表紙タイトル:Hyperbolicity & sensitive chaotic dynamics at homoclinic bifurcations
一般注記 Includes bibliographical references and index
著者標目 *Palis, Jacob, 1940-
Takens, Floris, 1940-
件 名 LCSH:Bifurcation theory
LCSH:Differentiable dynamical systems
LCSH:Chaotic behavior in systems
書誌ID 1000059131
ISBN 0521390648
NCID BA20353153
巻冊次 ISBN:0521390648
登録日 2009.09.10
更新日 2009.09.17

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