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Fully Chaotic Maps and Broken Time Symmetry : Nonlinear Phenomena and Complex Systems - Dean J. Driebe

Fully Chaotic Maps and Broken Time Symmetry

Nonlinear Phenomena and Complex Systems

Hardcover Published: 28th February 1999
ISBN: 9780792355649
Number Of Pages: 166

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This is the first book providing an introduction to a new approach to the nonequilibrium statistical mechanics of chaotic systems. It shows how the dynamical problem in fully chaotic maps may be solved on the level of evolving probability densities. On this level, time evolution is governed by the Frobenius-Perron operator. Spectral decompositions of this operator for a variety of systems are constructed in generalized function spaces. These generalized spectral decompositions are of special interest for systems with invertible trajectory dynamics, as on the statistical level the new solutions break time symmetry and allow for a rigorous understanding of irreversibility. Several techniques for the construction of explicit spectral decompositions are given. Systems ranging from the simple one-dimensional Bernoulli map to an invertible model of deterministic diffusion are treated in detail. Audience: Postgraduate students and researchers in chaos, dynamical systems and statistical mechanics.

Chaos and Irreversibilityp. 1
Statistical Mechanics of Mapsp. 11
The Bernoulli Mapp. 19
Other One-Dimensional Mapsp. 45
Intrinsic Irreversibilityp. 81
Deterministic Diffusionp. 93
Afterwordp. 115
A: Appendicesp. 117
Indexp. 162
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792355649
ISBN-10: 0792355644
Series: Nonlinear Phenomena and Complex Systems
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 166
Published: 28th February 1999
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 0.94