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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Generic Morse-Smale diffeomorphisms have only trivial symmetries


Author: Yoshio Togawa
Journal: Proc. Amer. Math. Soc. 65 (1977), 145-149
MSC: Primary 58F99
MathSciNet review: 0448449
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Abstract: The purpose of this paper is to prove that for a $ {C^1}$-generic Morse-Smale diffeomorphism f, the set of symmetries of f, $ Z(f)$, is equal to $ \{ {f^k}\vert k \in {\mathbf{Z}}\} $.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0448449-2
PII: S 0002-9939(1977)0448449-2
Keywords: Morse-Smale diffeomorphism, symmetry, centralizer, trivial symmetry, proper symmetry
Article copyright: © Copyright 1977 American Mathematical Society