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Characterisations of Ω-stability and structural stability via inverse shadowing

Published online by Cambridge University Press:  17 April 2009

Taeyoung Choi ,
Keonhee Lee  and
Yong Zhang
Taeyoung Choi
Affiliation:
Department of Mathematics, Chungnam National University, Daejeon, 305–764, Korea e-mail: [email protected], [email protected]
Keonhee Lee
Affiliation:
Department of Mathematics, Chungnam National University, Daejeon, 305–764, Korea e-mail: [email protected], [email protected]
Yong Zhang
Affiliation:
Department of Mathematics, Suzhou University, Suzhou, China e-mail: [email protected]
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We give characterisations of Ω-stable diffeomorphisms and structurally stable diffeomorphisms via the notions of weak inverse shadowing and orbital inverse shadowing, respectively. More precisely, it is proved that the C1 interior of the set of diffeomorphisms with the weak inverse shadowing property coincides with the set of Ω-stable diffeomorphisms and the C1 interior of the set of diffeomorphisms with the orbital inverse shadowing property coincides with the set of structurally stable diffeomorphisms.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 74 , Issue 2 , October 2006 , pp. 185 - 196
Copyright
Copyright © Australian Mathematical Society 2006

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