Fully chaotic maps and broken time symmetry
By: by Dean J. Driebe
Series: Nonlinear phenomena and complex systems -- v. 4
Publisher: Springer
Published: 2011
Place of publication: Dordrecht; London
Language: eng
Number of pages: 165
ISBN-13: 9789048151684
Subjects: Chaotic behavior in systems; Point mappings (Mathematics); Generalized spaces; Broken symmetry (Physics); Operator theory; Irreversible processes
Description: 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.
Notes: Originally published: 1999.

Includes bibliographical references and index.