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Tree maps with non divisible periodic orbits

Published online by Cambridge University Press:  17 April 2009

Xiangdong Ye
Xiangdong Ye
Affiliation:
Department of MathematicsUniversity of Science and Technology of ChinaHefei, Anhui 230026People's Republic of China, e-mail: yexd@sunlx06.nsc.ustc.edu.cn
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Abstract

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Let End (T) be the number of ends of a tree T and f: T → T be continuous. We show that f has a non divisible periodic orbit if and only if there are some x ∈ T and n > 1 with (n, m) = 1 for each 2 ≤ m ≤ End(T) such that x ∈ (f(x), fn(x)). Consequently the property of a tree map with a non divisible periodic orbit is preserved under small perturbation.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 3 , December 1997 , pp. 467 - 471
Copyright
Copyright © Australian Mathematical Society 1997

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