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Honary, Bahman,Bahabadi, Alireza Zamani Korean Mathematical Society 2008 대한수학회보 Vol.45 No.4
Let M be a generalized homogeneous compact space, and let Z(M) denotes the space of homeomorphisms of M with the $C^0$ topology. In this paper, we show that if the interior of the set of weak stable homeomorphisms on M is not empty then for any open subset W of Z(M) containing only weak stable homeomorphisms the orbital shadowing property is generic in W.
Bahman Honary,Alireza Zamani Bahabadi 대한수학회 2008 대한수학회보 Vol.45 No.4
Let M be a generalized homogeneous compact space, and let Z(M) denotes the space of homeomorphisms of M with the C0 topology. In this paper, we show that if the interior of the set of weak stable homeomorphisms on M is not empty then for any open subset W of Z(M) containing only weak stable homeomorphisms the orbital shadowing property is generic in W. Let M be a generalized homogeneous compact space, and let Z(M) denotes the space of homeomorphisms of M with the C0 topology. In this paper, we show that if the interior of the set of weak stable homeomorphisms on M is not empty then for any open subset W of Z(M) containing only weak stable homeomorphisms the orbital shadowing property is generic in W.
Weak Strictly Persistence Homeomorphisms and Weak Inverse Shadowing Property and Genericity
Honary, Bahman,Bahabadi, Alireza Zamani Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.3
In this paper we introduce the notions of strict persistence and weakly strict persistence which are stronger than those of persistence and weak persistence, respectively, and study their relations with shadowing property. In particular, we show that the weakly strict persistence and the weak inverse shadowing property are locally generic in Z(M).