Preimage entropy for random dynamical systems

被引：14
|
作者：
Zhu, Yujun [1 ]
机构：
[1] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
[2] Hebei Normal Univ, Coll Math & Informat Sci, Shijiazhuang, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2007年 / 18卷 / 04期
关键词：
random dynamical system; preimage entropy;
D O I：
10.3934/dcds.2007.18.829
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In [6]. Cheng and Newhouse introduced and studied the new invariants - preimage entropies for deterministic dynamical systems. In this paper, the analogous notions, measure-theoretic preimage entropy and topological preimage entropy, are formulated for random dynamical systems. Analogues of many known results for entropies, such as the Shannon-McMillan-Breiman Theorem, the Kolmogorov-Sinai Theorem, the Abromov-Rokhlin formula and the power rule, are obtained for preimage entropies. In particular, a variational principle is given.
引用
收藏
页码：829 / 851
页数：23
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