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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.


References [Enhancements On Off] (What's this?)

  • [1] R. Adler, A. Konheim and M. McAndrew, Topological entropy, Trans. Amer. Math. Soc. 114 (1965), 309-319. MR 0175106 (30:5291)
  • [2] L. Block, An example where topological entropy is continuous, Trans. Amer. Math. Soc. 231 (1977), 201-213. MR 0461582 (57:1567)
  • [3] -, Continuous maps of the interval with finite nonwandering set, Trans. Amer. Math. Soc. (to appear). MR 0474240 (57:13887)
  • [4] -, Topological entropy at an $ \Omega $-explosion, Trans. Amer. Math. Soc. (to appear). MR 0175106 (30:5291)
  • [5] R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401-414. MR 0274707 (43:469)
  • [6] -, Topological entropy and Axiom A, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, R.I., 1970, pp. 23-41. MR 0262459 (41:7066)
  • [7] R. Bowen and J. Franks, The periodic points of maps of the disc and the interval, Topology 15 (1976), 337-442. MR 0431282 (55:4283)

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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

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