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Topological sequence entropy for maps of the interval
Author(s):
Roman
Hric
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2045-2052.
MSC (1991):
Primary 26A18, 54H20, 58F13
Posted:
February 18, 1999
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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.
References:
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 -limit sets of maps of the interval with zero topological entropy, Ergod. Th. and Dynam. Sys. 13 (1993), 7 - 19. MR 94k:26006 - [F\v{S}S]
- Fedorenko, V. V., \v{S}arkovskii, A. N. and Smítal, J., Characterization of weakly chaotic maps of the interval, Proc. Amer. Math. Soc. 110 (1990), 141 - 148. MR 91a:58148
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- Franzová, N. and Smítal, J., Positive sequence entropy characterizes chaotic maps, Proc. Amer. Math. Soc. 112 (1991), 1083 - 1086. MR 91j:58107
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- Goodman, T. N. T., Topological sequence entropy, Proc. London Math. Soc. 29 (1974), 331 - 350. MR 50:8482
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![$[0,1]$](/proc/1999-127-07/S0002-9939-99-04799-1/gif-references/img416.gif) with zero topological entropy, Ergodic Theory (Oberwolfach 1978), Lecture Notes in Math. 729, Springer, 1979, pp. 144 - 152. MR 81a:28017 - [S]
- Smítal, J., Chaotic functions with zero topological entropy, Trans. Amer. Math. Soc. 297 (1986), 269 - 281. MR 87m:58107
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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:
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
Posted:
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
Copyright of article:
Copyright
1999,
American Mathematical Society
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