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Pointwise chain recurrent maps of the space Y

Published online by Cambridge University Press:  17 April 2009

Wenjing Guo ,
Fanping Zeng  and
Qiying Hu
Wenjing Guo
Affiliation:
School of Economics Management, Xidian University, Xi'an, Shanxi 710071, People's Republic of China
Fanping Zeng
Affiliation:
School of Economics Management, Xidian University, Xi'an, Shanxi 710071, People's Republic of China
Qiying Hu
Affiliation:
Institute of Mathematics, Guangxi University, Nanning, Gangxi 530004, People's Republic of China
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Abstract

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Let Y = {z ∈ C: z3 ∈ [0, 1]} (equipped with subspace topology of the complex space C) and let f: Y → Y be a continuous map. We show that if f is pointwise chain recurrent (that is, every point of Y is chain recurrent under f), then either f12 is the identity map or f12 is turbulent. This result is a generalisation to Y of a result of Block and Coven for pointwise chain recurrent maps of the interval.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 1 , February 2003 , pp. 79 - 85
Copyright
Copyright © Australian Mathematical Society 2003

References

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