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Dynamical Systems IX : Dynamical Systems with Hyperbolic Behaviour - D. V. Anosov

Dynamical Systems IX

Dynamical Systems with Hyperbolic Behaviour

By: D. V. Anosov (Editor), G.G. Gould (Translator)

Hardcover Published: 18th August 1995
ISBN: 9783540570431
Number Of Pages: 236

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This volume is devoted to the "hyperbolic theory" of dynamical systems (DS), that is, the theory of smooth DS's with hyperbolic behaviour of the tra- jectories (generally speaking, not the individual trajectories, but trajectories filling out more or less "significant" subsets in the phase space. Hyperbolicity the property that under a small displacement of any of a trajectory consists in point of it to one side of the trajectory, the change with time of the relative positions of the original and displaced points resulting from the action of the DS is reminiscent of the mot ion next to a saddle. If there are "sufficiently many" such trajectories and the phase space is compact, then although they "tend to diverge from one another" as it were, they "have nowhere to go" and their behaviour acquires a complicated intricate character. (In the physical literature one often talks about "chaos" in such situations. ) This type of be- haviour would appear to be the opposite of the more customary and simple type of behaviour characterized by its own kind of stability and regularity of the motions (these words are for the moment not being used as a strict ter- 1 minology but rather as descriptive informal terms). The ergodic properties of DS's with hyperbolic behaviour of trajectories (Bunimovich et al. 1985) have already been considered in Volume 2 of this series. In this volume we therefore consider mainly the properties of a topological character (see below 2 for further details).

Elliptic Boundary Problems
Boundary Value Problems for Elliptic Pseudodifferential Operators
Elliptic Boundary Value Problems in Domains with Piecewise Smooth Boundary
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540570431
ISBN-10: 3540570438
Series: Encyclopaedia of Mathematical Sciences
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 236
Published: 18th August 1995
Publisher: SPRINGER VERLAG GMBH
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.6
Weight (kg): 0.53

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