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Non-wandering points and the depth of a graph map

Part of: Connections with other structures, applications

Published online by Cambridge University Press:  09 April 2009

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

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Lef: G → G be a continuous map of a graph and let d(A) denote the derived set (or limit points) of A ⊂ G. We prove that d(Ω(f)) ⊂ λ (f) and the depth of f is at most three. We also prove that if f is piecewise monotone or has zero topological entropy, then the depth of f is at most two. Furthermore, we obtain some results on the topological structure of Ω(f).

Keywords

non-wandering pointgraphdepth of a graph map

MSC classification

Secondary: 54H20: Topological dynamics
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 69 , Issue 2 , October 2000 , pp. 143 - 152
Copyright
Copyright © Australian Mathematical Society 2000

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