Overview

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.

Full Product Details

Author:   Dean J. Driebe
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of the original 1st ed. 1999
Volume:   4
Dimensions:   Width: 15.50cm , Height: 0.90cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9789048151684

ISBN 10:   9048151686
Pages:   166
Publication Date:   06 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

1 Chaos and Irreversibility.- 2 Statistical Mechanics of Maps.- 3 The Bernoulli Map.- 4 Other One-Dimensional Maps.- 5 Intrinsic Irreversibility.- 6 Deterministic Diffusion.- 7 Afterword.- A Appendices.- A.1 Complex Microstructure of Phase Space.- A.2 More on Mixing.- A.4 Dual States.- A.5 The Resolvent Formalism.- A.6 Resealed Legendre Polynomials.- A.7 Formal Expression for the Eigenstates.- A.8 Explicit Evaluation of Eigenpolynomials.- A.9 Bernoulli Polynomials.- A.10 Generating Function Technique.- A.11 Jordan States.- A.12 Dual States of Jordan States.- A.13 Shift Polynomial Duals.- A.14 Symmetries in a Class of One-Dimensional Maps.- A.15 Invariant Measure of the Cantor Map.- A.17 Decomposition with Asymptotic Periodicity.- A.18 Frobenius—Perron Operator of the Baker Map.- A.19 Green—Kubo Formalism for the Multi-Bernoulli map.- A.20 Frobenius—Perron Operator of the Multi-Bernoulli map.- A.21 Eigenstates of the Full Multi-Bernoulli Map.

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