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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The $C^1$ closing lemma for
nonsingular endomorphisms equivariant under
free actions of finite groups


Authors: Xiaofeng Wang and Duo Wang
Journal: Trans. Amer. Math. Soc. 351 (1999), 4173-4182
MSC (1991): Primary 58F10, 58F20, 58F22, 58F35
Published electronically: March 18, 1999
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper a closing lemma for $C^1$ nonsingular endomorphisms equivariant under free actions of finite-groups is proved. Hence a recurrent trajectory, as well as all of its symmetric conjugates, of a $C^1$ nonsingular endomorphism equivariant under a free action of a finite group can be closed up simultaneously by an arbitrarily small $C^1$ equivariant perturbation.


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Additional Information

Xiaofeng Wang
Affiliation: Department of Applied Mathematics, Tsinghua University, Beijing 100084, P.R. China
Email: xfwang@math.tsinghua.edu.cn

Duo Wang
Affiliation: School of Mathematical Science, Peking University, Beijing 1000871, P.R. China
Email: dwang@sxx0.math.pku.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02199-6
PII: S 0002-9947(99)02199-6
Keywords: Periodic orbit, group action
Received by editor(s): February 21, 1997
Published electronically: March 18, 1999
Additional Notes: This work is supported by NNSF of China.
Article copyright: © Copyright 1999 American Mathematical Society