CONTINUUM-WISE EXPANSIVENESS AND SPECIFICATION FOR SET-VALUED FUNCTIONS AND TOPOLOGICAL ENTROPY

被引：22

作者：

Cordeiro, Welington ^{[1
]}

Pacifico, Maria Jose ^{[2
]}

机构：

[1] Penn State Univ, Dept Math, State Coll, PA 16802 USA

[2] Univ Fed Rio de Janeiro, Inst Matemat, CP 68-530, BR-21945970 Rio De Janeiro, RJ, Brazil

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 10期

关键词：

Continuum-wise expansiveness; set-valued functions; entropy; specification property; HOMEOMORPHISMS; DIMENSION; FLOWS;

D O I：

10.1090/proc/13168

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We define the concept of continuum-wise expansiveness for setvalued functions. We prove that for a compact metric space X with positive topological dimension, if a set-valued function is cw-expansive, then its topological entropy is positive. We also introduce the notion of point-wise specification property for set-valued functions and prove that set-valued functions with this property have positive entropy.

引用

页码：4261 / 4271

页数：11

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