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    Topological Dynamics of Random Dynamical Systems

    Topological Dynamics of Random Dynamical Systems by Cong, Nguyen Dinh;

    Series: Oxford Mathematical Monographs;

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    Product details:

    • Publisher OUP Oxford
    • Date of Publication 24 July 1997
    • Number of Volumes laminated boards

    • ISBN 9780198501572
    • Binding Hardback
    • No. of pages212 pages
    • Size 242x161x16 mm
    • Weight 442 g
    • Language English
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    Short description:

    This book is a systematic presentation of the solution of one of the fundamental problems of the theory of random dynamical systems - the problem of topological classification and structural stability of linear hyperbolic random dynamical systems.

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    Long description:

    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 the classical 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 dynamics of 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 structural stability 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.

    Topological conjugacy, classification and structural stability of linear hyperbolic random dynamical systems are investigated systematically and in detail.

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    Table of Contents:

    Introduction
    Deterministic dynamic systems
    Random dynamical systems: Foundations
    Linearization of nonlinear random dynamical systems
    Topological classification. Discrete-time case
    Structural stability. Continuous-time case
    Classification. Continuous-time case
    Topological invariants of linear cocycles
    References
    Index

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