On the dynamics of generic maps on the Cantor set

被引:2
|
作者
Kupka, Jiri [1 ]
Oprocha, Piotr [1 ,2 ]
机构
[1] Natl Supercomp Ctr IT4Innovat, Inst Res & Applicat Fuzzy Modeling, 30 Dubna 22, CZ-70103 Ostrava, Czech Republic
[2] AGH Univ Sci & Technol, Fac Appl Math, Al Mickiewicza 30, PL-30059 Krakow, Poland
关键词
Cantor set; Generic properties; Graph representation; Perturbations; TOPOLOGICAL-ENTROPY;
D O I
10.1016/j.topol.2019.05.029
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Recently Bernardes and Darji provided a very nice characterization of a residual set of maps of Cantor set in terms of covers of special type. Using their characterization, we provide a more direct description of this class. This way we are able to provide a further characterization of dynamical properties (e.g. shadowing properties, nullness) of maps in the class and further study of what features (e.g. prescribed minimal sets or the values of topological entropy) we can get by small perturbations of a given homeomorphism. (C) 2019 Elsevier B.V. All rights reserved.
引用
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页码:330 / 342
页数:13
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