Positively measure-expansive differentiable maps

详细信息    查看全文

• 作者：Keonhee Lee^a ; ^{khlee@cnu.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Manseob Lee^b ; ^{lmsds@mokwon.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Kazumine Moriyasu^c ; ^{moriyasu@ias.tokushima-u.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Kazuhiro Sakai^d ; ^{kazsakai@cc.utsunomiya-u.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Positively expansive maps ; Measure-expansive ; Expanding maps
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 March 2016
• 年：2016
• 卷：435
• 期：1
• 页码：492-507
• 全文大小：443 K

文摘

Let C¹(M)$C^1(M)$ be the space of differentiable maps of a closed C^∞$C^{\infty }$ manifold M   endowed with the C¹$C^1$-topology, and let f∈C¹(M)$f\in C^1(M)$. The purpose of this paper is to characterize the dynamics of positively measure-expansive differentiable maps from the measure theoretical view point. We show that (i) f   is in the C¹$C^1$-interior of the set of differentiable maps that is positively μ-expansive for any non-atomic Borel probability measure μ if and only if f   is expanding, and (ii) C¹$C^1$-generically, f is positively μ-expansive for any non-atomic Borel probability measure μ if and only if f is expanding.