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Topological horseshoes
Author(s):
Judy
Kennedy;
James
A.
Yorke
Journal:
Trans. Amer. Math. Soc.
353
(2001),
2513-2530.
MSC (1991):
Primary 58F12, 54F20;
Secondary 54F50, 58F20
Posted:
February 15, 2001
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Abstract:
When does a continuous map have chaotic dynamics in a set  ? More specifically, when does it factor over a shift on  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  . If that number is  and  , then  contains a compact invariant set which factors over a shift on  symbols.
References:
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Additional Information:
Judy
Kennedy
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
Email:
jkennedy@math.udel.edu
James
A.
Yorke
Affiliation:
Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742
Email:
yorke@ipst.umd.edu
DOI:
10.1090/S0002-9947-01-02586-7
PII:
S 0002-9947(01)02586-7
Keywords:
Topological horseshoe,
geometric horseshoe,
chaos,
shift dynamics,
connection,
preconnection,
crossing number,
expander,
symbol set.
Received by editor(s):
March 16, 1998
Received by editor(s) in revised form:
December 21, 1998
Posted:
February 15, 2001
Additional Notes:
This research was supported by the National Science Foundation, Division of Mathematical Sciences
Copyright of article:
Copyright
2001,
American Mathematical Society
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