Smooth Ergodic Theory of Random Dynamical Systems
Smooth Ergodic Theory of Random Dynamical Systems
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DOI：
10.1007/bfb0094308
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发表时间：
1995-09
期刊：
影响因子：
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通讯作者：
Pei-dong Liu;M. Qian
中科院分区：
文献类型：
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作者：
Pei-dong Liu;M. Qian
本书研究随机动态系统（即带有噪声的确定性系统）的遍历理论方面。它旨在系统地处理一系列有关此类系统的不变测度、熵和李亚普诺夫指数的最新结果，并且可以被视为基弗著作的更新。佩辛类型的熵公式占据了中心部分。关系数的介绍（第 2 章）是原创的，书中涉及的大多数方法都是动力系统或测度论中的规范方法。本书面向对噪声扰动动态系统感兴趣的人们，并且可以为进一步研究该主题铺平道路。假设具有微分几何、测度论、遍历理论、动力系统和最好的随机过程的合理知识。
This book studies ergodic-theoretic aspects of random dynam-ical systems, ie 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.