The Topology of Chaos

beimu1009

* Title: The Topology of Chaos: Alice in Stretch and Squeezeland
    * Authors: Robert Gilmore, Marc Lefranc
    * Pages: 518 pages
    * Publisher: Wiley-Interscience; 1st edition (June 15, 2002)
    * Language: English
    * ISBN-10: 0471408166
    * ISBN-13: 978-0471408161

Book Description
A new approach to understanding nonlinear dynamics and strange attractors
The behavior of a physical system may appear irregular or chaotic evenwhen it is completely deterministic and predictable for short periodsof time into the future. How does one model the dynamics of a systemoperating in a chaotic regime? Older tools such as estimates of thespectrum of Lyapunov exponents and estimates of the spectrum of fractaldimensions do not sufficiently answer this question. In a significantevolution of the field of Nonlinear Dynamics, The Topology of Chaosresponds to the fundamental challenge of chaotic systems by introducinga new analysis method-Topological Analysis-which can be used toextract, from chaotic data, the topological signatures that determinethe stretching and squeezing mechanisms which act on flows in phasespace and are responsible for generating chaotic data. Beginning withan example of a laser that has been operated under conditions in whichit behaved chaotically, the authors convey the methodology ofTopological Analysis through detailed chapters on:
* Discrete Dynamical Systems: Maps
* Continuous Dynamical Systems: Flows
* Topological Invariants
* Branched Manifolds
* The Topological Analysis Program
* Fold Mechanisms
* Tearing Mechanisms
* Unfoldings
* Symmetry
* Flows in Higher Dimensions
* A Program for Dynamical Systems Theory
Suitable at the present time for analyzing “strange attractors” thatcan be embedded in three-dimensional spaces, this groundbreakingapproach offers researchers and practitioners in the discipline acomplete and satisfying resolution to the fundamental questions ofchaotic systems.

游客，本帖隐藏的内容需要积分高于 1 才可浏览，您当前积分为 0