Everywhere chaotic homeomorphisms on manifolds and k-dimensional Menger manifolds

被引：30

作者：

Kato, H ^{[1
]}

机构：

[1] UNIV TSUKUBA,INST MATH,TSUKUBA,IBARAKI 305,JAPAN

来源：

TOPOLOGY AND ITS APPLICATIONS | 1996年 / 72卷 / 01期

关键词：

sensitive dependence on initial conditions; shift map; attractor; Menger compactum; UVk-map; Z-set; near homeomorphism;

D O I：

10.1016/0166-8641(96)00008-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce a new notion of everywhere chaotic homeomorphism and we prove that any compact connected topological n-manifold (n greater than or equal to 2) and any compact connected k-dimensional Menger manifold (k greater than or equal to 1) admit everywhere chaotic homeomorphisms. All constructions of such homeomorphisms essentially rely on one-dimensional maps and the method comes from an idea of Barge and Martin (1990).

引用

页码：1 / 17

页数：17

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