Abstract
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.
Publisher
Cambridge University Press (CUP)
Reference4 articles.
1. Morimoto A. , Stochastic stable diffeomorphisms and Takens’ conjecture, to appear.
2. ω-Limit sets for Axiom A diffeomorphisms
3. On semi-stability for diffeomorphisms
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31 articles.
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