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

Author(s): Xiaofeng Wang; Duo Wang
Journal: Trans. Amer. Math. Soc. 351 (1999), 4173-4182.
MSC (1991): Primary 58F10, 58F20, 58F22, 58F35
Posted: March 18, 1999
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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: 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
Posted: March 18, 1999
Additional Notes: This work is supported by NNSF of China.
Copyright of article: Copyright 1999, American Mathematical Society

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