Authors
Citation
J. Kennedy et Ja. Yorke, Topological horseshoes, T AM MATH S, 353(6), 2001, pp. 2513-2530
Citations number
8
Categorie Soggetti
Mathematics
Journal title
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029947
→ ACNP
Volume
353
Issue
6
Year of publication
2001
Pages
2513 - 2530
Database
ISI
SICI code
0002-9947(2001)353:6<2513:TH>2.0.ZU;2-5
Abstract
When does a continuous map have chaotic dynamics in a set Q? More specifica
lly, when does it factor over a shift on M symbols? This paper is an attemp
t 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 factor
s over a shift on M symbols.