Topological Dynamics of Random Dynamical Systems

Hardcover | July 24, 1997

EditorNguyen Dinh Nguyen Dinh Cong

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This book is devoted to the theory of topological dynamics of random dynamical systems. The theory of random dynamical systems is a relatively new and fast expanding field of research which attracts the attention of researchers from various fields of science. It unites and develops theclassical deterministic theory of dynamical systems and probability theory, hence finding many applications in a very wide range of disciplines from physics to biology to engineering, finance, and economics. Recent developments call for a systematic presentation of the theory. Topological dynamicsof random dynamical systems is the first book to deal with the theory of topological dynamics of random dynamical systems. It presents in detail the solutions to the most fundamental problems of topological dynamics: linearization of nonlinear smooth systems, classification, and structuralstability of linear hyperbolic systems. Employing the tools and methods of algebraic ergodic theory, the theory presented in the book has surprisingly beautiful results showing the richness of random dynamical systems as well as giving a gentle generalization of the classical deterministic theory.Mathematicians working in the theory of dynamical systems, stochastic dynamics, as well as those interested in applications of mathematical systems with random noise, will find this timely book a valuable reference and rich source of modern mathematical results and methods.

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From the Publisher

This book is devoted to the theory of topological dynamics of random dynamical systems. The theory of random dynamical systems is a relatively new and fast expanding field of research which attracts the attention of researchers from various fields of science. It unites and develops theclassical deterministic theory of dynamical syste...

Nguyen Dinh Cong is at University of Bremen.

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Format:HardcoverDimensions:212 pages, 9.21 × 6.14 × 0.63 inPublished:July 24, 1997Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198501579

ISBN - 13:9780198501572

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Table of Contents

Introduction1. Deterministic dynamic systems2. Random dynamical systems: Foundations3. Linearization of nonlinear random dynamical systems4. Topological classification. Discrete-time case5. Structural stability. Continuous-time case7. Classification. Continuous-time case8. Topological invariants of linear cocyclesReferencesIndex

Editorial Reviews

`Topological conjugacy, classification and structural stability of linear hyperbolic random dynamical systems are investigated systematically and in detail.'Zentralblatt fur Mathematik