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Pointwise-recurrent graph maps

Published online by Cambridge University Press:  02 February 2005

JIE-HUA MAI
JIE-HUA MAI
Affiliation:
Institute of Mathematics, Shantou University, Shantou, Guangdong, 515063, People's Republic of China (e-mail: [email protected])
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Abstract

In this paper we show that a continuous map f from a connected graph G to itself is pointwise-recurrent if and only if one of the following two statements holds: (1) G is a circle, and f is a homeomorphism topologically conjugate to an irrational rotation of the unit circle S1; (2) f is a periodic homeomorphism.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 2 , April 2005 , pp. 629 - 637
Copyright
2005 Cambridge University Press

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