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Field name	Details
Dewey Class	515
Title	Random Dynamical Systems ([EBook]) / by Ludwig Arnold.
Author	Arnold, Ludwig. , 1937-
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 1998.
Physical Details	XV, 586 pages : online resource.
Series	Springer monographs in mathematics 1439-7382
ISBN	9783662128787
Summary Note	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.:
Contents note	I. Random Dynamical Systems and Their Generators -- 1. Basic Definitions. Invariant Measures -- 2. Generation -- II. Multiplicative Ergodic Theory -- 3. The Multiplicative Ergodic Theorem in Euclidean Space -- 4. The Multiplicative Ergodic Theorem on Bundles and Manifolds -- 5. The MET for Related Linear and Affine RDS -- 6. RDS on Homogeneous Spaces of the General Linear Group -- III. Smooth Random Dynamical Systems -- 7. Invariant Manifolds -- 8. Normal Forms -- 9. Bifurcation Theory -- IV. Appendices -- Appendix A. Measurable Dynamical Systems -- A.1 Ergodic Theory -- A.2 Stochastic Processes and Dynamical Systems -- A.3 Stationary Processes -- A.4 Markov Processes -- Appendix B. Smooth Dynamical Systems -- B.1 Two-Parameter Flows on a Manifold -- B.4 Autonomous Case: Dynamical Systems -- B.5 Vector Fields and Flows on Manifolds -- References.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-662-12878-7
Links to Related Works	Subject References: Analysis (Mathematics) . Dynamical Systems . Dynamical systems and ergodic theory . Dynamics . Ergodic theory . Integral Equations . Mathematical analysis . Probabilities . Statistical Physics . System theory . Authors: Arnold, Ludwig. 1937- . Arnold, Ludwig, 1937- . Corporate Authors: SpringerLink (Online service) . Series: Springer monographs in mathematics . Classification: 515 .

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Random Dynamical Systems

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