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＜電子ブック＞
Smooth Ergodic Theory of Random Dynamical Systems / by Pei-Dong Liu, Min Qian
(Lecture Notes in Mathematics. ISSN:16179692 ; 1606)

版	1st ed. 1995.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1995
大きさ	XII, 228 p : online resource
著者標目	*Liu, Pei-Dong author Qian, Min author SpringerLink (Online service)
件　名	LCSH:Manifolds (Mathematics) LCSH:Probabilities LCSH:System theory LCSH:Thermodynamics LCSH:Mathematical physics FREE:Manifolds and Cell Complexes FREE:Probability Theory FREE:Complex Systems FREE:Thermodynamics FREE:Theoretical, Mathematical and Computational Physics
一般注記	Preliminaries -- Entropy and Lyapunov exponents of random diffeomorphisms -- Estimation of entropy from above through Lyapunov exponents -- Stable invariant manifolds of random diffeomorphisms -- Estimation of entropy from below through Lyapunov exponents -- Stochastic flows of diffeomorphisms -- Characterization of measures satisfying entropy formula -- Random perturbations of hyperbolic attractors This book studies ergodic-theoretic aspects of random dynam- ical systems, i.e. of deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems, and can be viewed as an update of Kifer's book. An entropy formula of Pesin's type occupies the central part. The introduction of relation numbers (ch.2) is original and most methods involved in the book are canonical in dynamical systems or measure theory. The book is intended for people interested in noise-perturbed dynam- ical systems, and can pave the way to further study of the subject. Reasonable knowledge of differential geometry, measure theory, ergodic theory, dynamical systems and preferably random processes is assumed HTTP:URL=https://doi.org/10.1007/BFb0094308

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