Generic continuity of metric entropy for volume-preserving diffeomorphisms

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:425

Article

Yang, Jiagang¹  Zhou, Yunhua² 

[1] Univ Fed Fluminense, Inst Matemat & Estat, Dept Geomet, BR-24020140 Niteroi, RJ, Brazil

[2] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China

关键词: Continuity;    Metric entropy;    Volume-preserving;   

DOI  :  10.1016/j.jmaa.2014.12.032

来源: Elsevier

【 摘 要 】

Let M be a compact manifold and Diff(m)(1) (M) be the set of C-1 volume-preserving diffeomorphisms of M. We prove that there is a residual subset R subset of Diff(m)(1) (M) such that each f is an element of R. is a continuity point of the map g -> h(m)(g) from Diff(m)(1) (M) to R, where h(m)(g) is the metric entropy of g with respect to volume measure m. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free