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Random Dynamical Systems (Springer Monographs in Mathematics)

Arnold, Ludwig

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ISBN 10: 3540637583 / ISBN 13: 9783540637585
Verlag: Springer, 2003
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Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: I. Random Dynamical Systems and Their Generators: Basic Definitions. Invariant Measures. Generation.- II. Multiplicative Ergodic Theory:in Euclidean Space, on Bundles,for Rela ted Linear Random Dynamical Systems, Random Dynamcial Systems on Homogeneous Spaces. III. Smooth Random Dynamical Systems: Invariant Manifolds, Normal Forms, Bifurcation Theory. IV. Appendices: Measurable Systems, Smooth Dynamical Systems. Buchnummer des Verkäufers ABE_book_new_3540637583

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Inhaltsangabe:

The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.

Klappentext: 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.

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Bibliografische Details

Titel: Random Dynamical Systems (Springer ...

Verlag: Springer

Erscheinungsdatum: 2003

Einband: Hardcover

Zustand: New

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