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 | References | Similar Articles | Additional Information

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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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