Springer Monographs in Mathematics

Random Dynamical Systems

Authors: Arnold, Ludwig

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  • ISBN 978-3-662-12878-7
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About this book

This book is the first systematic presentation of the theory of random dynamical systems, i.e. of dynamical systems under the influence of some kind of randomness. The theory comprises products of random mappings as well as random and stochastic differential equations. The author's approach is based on Oseledets'multiplicative ergodic theorem for linear random systems, for which a detailed proof is presented. This theorem provides us with a random substitute of linear algebra and hence can serve as the basis of a local theory of nonlinear random systems. In particular, global and local random invariant manifolds are constructed and their regularity is proved. Techniques for simplifying a system by random continuous or smooth coordinate tranformations are developed (random Hartman-Grobman theorem, random normal forms). Qualitative changes in families of random systems (random bifurcation theory) are also studied. A dynamical approach is proposed which is based on sign changes of Lyapunov exponents and which extends the traditional phenomenological approach based on the Fokker-Planck equation. Numerous instructive examples are treated analytically or numerically. The main intention is, however, to present a reliable and rather complete source of reference which lays the foundations for future works and applications.

Reviews

"Ludwig Arnold's monograph is going to make a very big impact for many years to come."
DMV Jahresbericht, 103. Band, Heft 2, July 2001

Table of contents (9 chapters)

  • Basic Definitions. Invariant Measures

    Arnold, Ludwig

    Pages 3-47

  • Generation

    Arnold, Ludwig

    Pages 49-107

  • The Multiplicative Ergodic Theorem in Euclidean Space

    Arnold, Ludwig

    Pages 111-162

  • The Multiplicative Ergodic Theorem on Bundles and Manifolds

    Arnold, Ludwig

    Pages 163-199

  • The MET for Related Linear and Affine RDS

    Arnold, Ludwig

    Pages 201-233

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-662-12878-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-540-63758-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-3-642-08355-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Random Dynamical Systems
Authors
Series Title
Springer Monographs in Mathematics
Copyright
1998
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-12878-7
DOI
10.1007/978-3-662-12878-7
Hardcover ISBN
978-3-540-63758-5
Softcover ISBN
978-3-642-08355-6
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XV, 586
Topics