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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Mappings of the interval with finitely many periodic points have zero entropy


Author: Louis Block
Journal: Proc. Amer. Math. Soc. 67 (1977), 357-360
MSC: Primary 58F20; Secondary 54H20
DOI: https://doi.org/10.1090/S0002-9939-1977-0467841-3
MathSciNet review: 0467841
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Abstract: It is shown that if f is a continuous map of a closed interval into itself, and f has finitely many periodic points, then the topological entropy of f is zero.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0467841-3
Keywords: Topological entropy, periodic point, nonwandering set, unstable manifold
Article copyright: © Copyright 1977 American Mathematical Society