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Topologically stable homeomorphisms of the circle

Published online by Cambridge University Press:  22 January 2016

Koichi Yano
Koichi Yano*
Affiliation:
Department of Mathematics, Faculty of Science, University of Tokyo
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In this paper, we study topologically stable homeomorphisms of the circle. Our results are the following:

Theorem 1. A homeomorphism of the circle is topologically stable if and only if it is topologically conjugate to some Morse-Smale diffeomorphism.

Theorem 2. There exists a homeomorphism of the circle which has the pseudo-orbit-tracing-property but is not topologically stable.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 79 , October 1980 , pp. 145 - 149
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1980

References

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[ 2 ] Morimoto, A., Stochastic stable diffeomorphisms and Takens’ conjecture, to appear.Google Scholar
[ 3 ] Nitecki, Z., On semi-stability for diffeomorphisms, Inv. Math., 14 (1971), 81–122.CrossRefGoogle Scholar
[ 4 ] Nitecki, Z., Differentiate dynamics, M.I.T. Press (1971).Google Scholar