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

被引：17
|
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.
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页码：4261 / 4271
页数：11
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