Weak shadowing for discrete dynamical systems on nonsmooth manifolds |
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Authors: | Marcin Mazur |
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Institution: | Uniwersytet Jagielloński, Instytut Matematyki, Reymonta 4, 30-059 Kraków, Poland |
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Abstract: | In J. Math. Anal. Appl. 189 (1995) 409-423, Corless and Pilyugin proved that weak shadowing is a C0 generic property in the space of discrete dynamical systems on a compact smooth manifold M. In our paper we give another proof of this theorem which does not assume that M has a differential structure. Moreover, our method also works for systems on some compact metric spaces that are not manifolds, such as a Hilbert cube (or generally, a countably infinite Cartesian product of manifolds with boundary) and a Cantor set. |
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Keywords: | (Weak) shadowing (Discrete) dynamical system Pseudo-trajectory Homogeneity Generic property |
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