Topological horseshoes

被引：151

作者：

Kennedy, J ^{[1
]}

Yorke, JA

机构：

[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[2] Univ Maryland, Inst Phys Sci & Technol, College Pk, MD 20742 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2001年 / 353卷 / 06期

关键词：

topological horseshoe; geometric horseshoe; chaos; shift dynamics; connection; preconnection; crossing number; expander; symbol set;

D O I：

10.1090/S0002-9947-01-02586-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

When does a continuous map have chaotic dynamics in a set Q? More specifically, when does it factor over a shift on M symbols? This paper is an attempt to clarify some of the issues when there is no hyperbolicity assumed. We find that the key is to define a "crossing number" for that set Q. If that number is M and M > 1, then Q contains a compact invariant set which factors over a shift on M symbols.

引用

页码：2513 / 2530

页数：18

共 9 条

[1] A GEOMETRIC CRITERION FOR POSITIVE TOPOLOGICAL-ENTROPY [J].