Fully Chaotic Maps and Broken Time Symmetry

Download or read book Fully Chaotic Maps and Broken Time Symmetry written by Dean J. Driebe and published by Springer Science & Business Media. This book was released on 1999-02-28 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.