雙曲混沌

內容概要

本書從物理學而不是數學概念的角度介紹了目前動力系統(tǒng)中均勻雙曲吸引子研究的進展小結構穩(wěn)定的吸引子表現出強烈的隨機性，但是對于動力系統(tǒng)中函數和參數的變化不敏感?；陔p曲混沌的特征，本書將展示如何找到物理系統(tǒng)中的雙曲混沌吸引子，以及怎樣設計具有雙曲混沌的物理系統(tǒng)。
本書可以作為研究生和高年級本科生教材，也可以供大學教授以及物理學、機械學和工程學相關研究人員參考。

作者簡介

　　Kuznetsov博士是非線性和混沌動力學方面的著名科學家。他是俄羅斯薩拉托夫國立大學非線性過程系的教授，已經出版了三本混沌動力學及其應用方面的專著。

書籍目錄

Part I Basic Notions and Review
Part II Low-Dimensional Models
Part III Higher-Dimensional Systems and Phenomena
Part IV Experimental Studies
Appendix A Computation of Lyapunov Exponents:The Benettin
Algorithm
Appendix B Henon and Ikeda Maps
 References
Appendix C Smale's Horseshoe and Homoclinic Tangle
 References
Appendix D Fractal Dimensions and Kaplan-Yorke Formula
 References
Appendix E Hunt's Model: Formal Definition
 References
Appendix F Geodesics on a Compact Surface of Negative
Curvature
 References
Appendix G Effect of Noise in a System with a Hyperbolic
Attractor
 References
Index

章節(jié)摘錄

版權頁：插圖：The epithet uniformly hyperbolic means that the rates of exponential growth of decay of magnitudes of vectors relating to the stable and unstable manifolds are bounded and detached from zero by some （globally defined） constants. In the phase space a set of trajectories, which approaches the reference orbit in the course of forward evolution in time, is called the stable manifold. Similarly, the unstable manifold is a set of trajectories, which approaches the reference orbit in reverse time. For hyperbolic orbits these sets are indeed manifolds, that means they are smooth objects like curves, surfaces or hyper-surfaces in the phase space; this is a conclusion of special theorem （known as the Hadamard-Perron theorem） （Anosov, 1967; Katok and Hasselblatt, 1995; Barreira and Pesin, 2001）.Uniformly hyperbolic saddle trajectories, and invariant sets composed of such trajectories may occur in phase spaces of both conservative and dissipative systems, but in this book we concentrate on the dissipative case. Hence, we will deal with such a kind of the hyperbolic invariant sets as the uniformly hyperbolic attractors.The uniformly hyperbolic attractor is a bounded attracting invariant set in the phase space of a dissipative system, composed exclusively of uniformly hyperbolic saddle trajectories, and near all these trajectories the phase space is arranged locally in one and the same manner. Manifolds for all trajectories belonging to the attrac-tor must have the same dimension. The intersections between stable and unstable manifolds are allowed only at nonzero angles （touches are excluded）.

編輯推薦

《雙曲混沌:一個物理學家的觀點(英文版)》為非線性物理科學之一。

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