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Chain recurrent points and topological entropy of a tree map

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Abstract

Let f be a tree map, P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper, the notion of division for invariant closed subsets of a tree map is introduced. It is proved that: (1) f has zero topological entropy if and only if for any xε CR(f)−P(f) and each natural number s the orbit of x under f s has a division; (2) If f has zero topological entropy, then for any x ε CR(f) − P(f) the θ-limit set of x is an infinite minimal set.

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Authors and Affiliations

  1. Dept. of Math., Guangxi Univ., 530004, Nanning

    Sun Taixiang

  2. Dept. of Math., Univ. of Science and Technology of China, 230026, Hefei, China

    Sun Taixiang

Authors
  1. Sun Taixiang
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Additional information

Supported by the National Natural Science Foundation of China (19961001) and SF of Guangxi (0135027).

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Sun, T. Chain recurrent points and topological entropy of a tree map. Appl. Math. Chin. Univ. 17, 313–318 (2002). https://doi.org/10.1007/s11766-002-0010-1

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  • DOI: https://doi.org/10.1007/s11766-002-0010-1

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