可数度量空间上的完全分布混沌映射

数学物理学报 ›› 2011, Vol. 31 ›› Issue (2): 298-304.

可数度量空间上的完全分布混沌映射

袁大琏|吕杰

南京师范大学数学系南京 210046；华南师范大学数学系广州 510631

收稿日期:2008-11-30 修回日期:2010-03-25 出版日期:2011-04-25 发布日期:2011-04-25
基金资助:
国家自然科学基金(10471049, 10771079) 资助

Completely Distributionally Chaotic Maps on Countable Metric Spaces

YUAN Da-Lian, LV Jie

School of Mathematics, Nanjing Normal University, Nanjing 210046|School of Mathematics, South China Normal University, Guangzhou |510631

Received:2008-11-30 Revised:2010-03-25 Online:2011-04-25 Published:2011-04-25
Supported by:
国家自然科学基金(10471049, 10771079) 资助

摘要/Abstract

摘要：

设X={x₀, x₁, …} 是一个自密的可数度量空间. 则对任意 0<δX, 存在X上的同胚φ 满足: (a)X={φⁱx₀:i ∈Z} 且{φⁱ x₀: i ≥0}, {φ-ⁱx₀: i≥0}
均为X 的稠密子集; (b) φ, φ^-1 均以 X为其一个分布式 δ -混沌集.

关键词: 可数度量空间, 完全分布混沌映射

Abstract:

Let X={x₀, x₁, …} be a countable metric space without isolate point. Then for every 0<δ<diam X there exists a homeomorphism φ on X such that (a) X={φⁱx₀: i ∈Z} and either {φⁱx₀: i ≥0} and {φ^-ⁱx₀: i ≥0} is dense in X and (b) X is a distributionally δ-chaotic set of either
φ or φ^-1.

Key words: Countable metric space, Completely distributionally chaotic map

中图分类号:

37B05

袁大琏, 吕杰. 可数度量空间上的完全分布混沌映射[J]. 数学物理学报, 2011, 31(2): 298-304.

YUAN Da-Lian, LV Jie. Completely Distributionally Chaotic Maps on Countable Metric Spaces[J]. Acta mathematica scientia,Series A, 2011, 31(2): 298-304.

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