Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations : fractal dimensions and infinitely many attractors
著者
書誌事項
Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations : fractal dimensions and infinitely many attractors
(Cambridge studies in advanced mathematics, 35)
Cambridge University Press, 1995, c1993
- : pbk
- タイトル別名
-
Hyperbolicity & sensitive chaotic dynamics at homoclinic bifurcations
大学図書館所蔵 全27件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references and index
内容説明・目次
内容説明
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 stimulate new developments, relating the theory of fractal dimensions to bifurcations, and concerning homoclinic bifurcations as generators of chaotic dynamics. To this end the authors finish the book with an account of recent research and point out future prospects. 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 Henon-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 coexistence of infinitely many periodic attractors, one of the deepest theorems in chaotic dynamics. Based on graduate courses, this unique book will be an essential purchase for students and research workers in dynamical systems, and also for scientists and engineers applying ideas from chaos theory and nonlinear dynamics.
目次
- Preface
- 1. Hyperbolicity, stability and sensitive-chaotic dynamical systems
- 2. Examples of homoclinic orbits in dynamical systems
- 3. Dynamical consequences of a transverse homoclinic intersection
- 4. Homoclinic tangencies: cascades of bifurcations, scaling and quadratic maps
- 5. Cantor sets in dynamics and fractal dimensions
- 6. Homoclinic bifurcations: fractal dimensions and measure of bifurcation sets
- 7. Infinitely many sinks and homoclinic tangencies
- 8. Overview, conjectures and problems - a theory of homoclinic bifurcations - strange attractors
- Appendices
- References.
「Nielsen BookData」 より