Smooth Ergodic Theory of Random Dynamical Systems (Paperback)

Pei-Dong Liu

ISBN 10: 3540600043 / ISBN 13: 9783540600046

Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin, 1995

Riguardo questo articolo

Paperback. This text studies ergodic-theoretic aspects of random dynamical systems, for example, 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. An entropy formula of Pesin's type occupies the central part of the text whilst chapter two introduces relation numbers highlighting canonical methods in dynamical systems and measure theory. The text is intended for readers interested in noise-perturbed dynamical systems and may indicate further areas of study. Reasonable knowledge of differetial geometry, measure theory, ergodic theory, dynamical systems and preferably random processees is assumed. This book studies ergodic-theoretic aspects of random dynam- ical systems, i.e. The introduction of relation numbers (ch.2) is original and most methods involved in the book are canonical in dynamical systems or measure theory. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9783540600046

Dati bibliografici

• Titolo: Smooth Ergodic Theory of Random Dynamical Systems (Paperback)
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin
• Data di pubblicazione: 1995
• Lingua: Inglese
• ISBN 10: 3540600043
• ISBN 13: 9783540600046
• Rilegatura: Paperback
• Condizione: new

Descrizione articolo

Riassunto

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.

Contenuti

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.