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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Maximal entropy odd orbit types


Authors: William Geller and Juán Tolosa
Journal: Trans. Amer. Math. Soc. 329 (1992), 161-171
MSC: Primary 58F20; Secondary 54C70, 54H20, 58F08
MathSciNet review: 1020040
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Abstract: A periodic orbit of a continuous map of an interval induces in a natural way a cyclic permutation, called its type. We consider a family of orbit types of period $ n$ congruent to $ 1$ ( $ \operatorname{mod} 4$) introduced recently by Misiurewicz and Nitecki. We prove that the Misiurewicz-Nitecki orbit types and their natural generalizations to the remaining odd periods $ n$ have maximal entropy among all orbit types of period $ n$, and even among all $ n$-permutations.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1020040-1
PII: S 0002-9947(1992)1020040-1
Keywords: Orbit type, entropy, cycle, Markov graph
Article copyright: © Copyright 1992 American Mathematical Society