Overview

Providing an introduction to a new approach to the non-equilibrium statistical mechanics of chaotic systems, this book 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. Several techniques for the construction of explicit spectral decompositions are given, such as those 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. Systems ranging from the simple one-dimensional Bernoulli map to an invertible model of deterministic diffusion are treated in detail.

Full Product Details

Author:   Dean J. Driebe
Publisher:   Springer
Imprint:   Springer
Edition:   1999 ed.
Volume:   4
Dimensions:   Width: 15.50cm , Height: 1.10cm , Length: 23.50cm
Weight:   0.940kg
ISBN:  

9780792355649

ISBN 10:   0792355644
Pages:   166
Publication Date:   28 February 1999
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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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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