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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Topological sequence entropy
for maps of the interval


Author: Roman Hric
Journal: Proc. Amer. Math. Soc. 127 (1999), 2045-2052
MSC (1991): Primary 26A18, 54H20, 58F13
Published electronically: February 18, 1999
MathSciNet review: 1487372
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Abstract: A result by Franzová and Smítal shows that a continuous map of the interval into itself is chaotic if and only if its topological sequence entropy relative to a suitable increasing sequence of nonnegative integers is positive. In the present paper we prove that for any increasing sequence of nonnegative integers there exists a chaotic continuous map with zero topological sequence entropy relative to this sequence.


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Additional Information

Roman Hric
Affiliation: Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK–974 01 Banská Bystrica, Slovak Republic
Email: hric@fpv.umb.sk

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04799-1
PII: S 0002-9939(99)04799-1
Keywords: Adding machine, blowing up orbits, chaotic map, topological sequence entropy
Received by editor(s): May 30, 1997
Received by editor(s) in revised form: October 2, 1997
Published electronically: February 18, 1999
Additional Notes: The author has been partially supported by the Slovak grant agency, grant number 1/1470/94.
Communicated by: Mary Rees
Article copyright: © Copyright 1999 American Mathematical Society