Fully Chaotic Maps and Broken Time Symmetry by Dean DriebeFully Chaotic Maps and Broken Time Symmetry by Dean Driebe

Fully Chaotic Maps and Broken Time Symmetry

byDean Driebe

Paperback | December 6, 2010

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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.
Title:Fully Chaotic Maps and Broken Time SymmetryFormat:PaperbackDimensions:175 pages, 9.25 × 6.1 × 0.68 inPublished:December 6, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048151686

ISBN - 13:9789048151684

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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. Appendices.