Smooth Ergodic Theory of Random Dynamical Systems

Min Qian

ISBN 10: 3540600043 / ISBN 13: 9783540600046

Editore: Springer Berlin Heidelberg, Springer Berlin Heidelberg, 1995

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Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9783540600046

Dati bibliografici

• Titolo: Smooth Ergodic Theory of Random Dynamical Systems
• Editore: Springer Berlin Heidelberg, Springer Berlin Heidelberg
• Data di pubblicazione: 1995
• Lingua: Inglese
• ISBN 10: 3540600043
• ISBN 13: 9783540600046
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 14 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 14 millimetri di profondità
• Peso: 371 grammi

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.