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Chain recurrent points of a tree map

Published online by Cambridge University Press:  17 April 2009

Tao Li  and
Xiangdong Ye
Tao Li
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, Peoples Republic of China e-mail: yexd@ustc.edu.cn
Xiangdong Ye
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, Peoples Republic of China e-mail: yexd@ustc.edu.cn
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Abstract

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We generalise a result of Hosaka and Kato by proving that if the set of periodic points of a continuous map of a tree is closed then each chain recurrent point is a periodic one. We also show that the topological entropy of a tree map is zero if and only if the w-limit set of each chain recurrent point (which is not periodic) contains no periodic points.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 2 , April 1999 , pp. 181 - 186
Copyright
Copyright © Australian Mathematical Society 1999

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