ON INVARIANT ε-SCRAMBLED SETS

被引：6

作者：

Balibrea, Francisco ^{[1
]}

Guirao, Juan L. G. ^{[2
]}

Oprocha, Piotr ^{[1
,3
]}

机构：

[1] Univ Murcia, Dept Matemat, E-30100 Murcia, Spain

[2] Univ Politecn Cartagena, Dept Matemat Aplicada & Estadist, Hosp Marina, Cartagena 30203, Spain

[3] AGH Univ Sci & Technol, Fac Appl Math, PL-30059 Krakow, Poland

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2010年 / 20卷 / 09期

关键词：

Topological mixing; scrambled set; Mycielski sets; proximal relation; Li-Yorke chaos; subshift; LI-YORKE CHAOS; DEVANEYS CHAOS; MAPS; HOMEOMORPHISMS; ENTROPY;

D O I：

10.1142/S0218127410027465

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This article is devoted to the study of invariant epsilon-scrambled sets. We show that every topologically mixing map with at least one fixed point contains at least one such set. Additionally we show that this condition can be weakened in the case of symbolic dynamics, e.g. mixing can be replaced by transitivity. Some relations between mixing and proximal relation are also studied.

引用

页码：2925 / 2935

页数：11

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