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April  2005, 12(3): 523-530. doi: 10.3934/dcds.2005.12.523

On $C^0$ genericity of various shadowing properties

Piotr Kościelniak 1, and  Marcin Mazur 1,

1. 

Uniwersytet Jagielloński, Instytut Matematyki, Reymonta 4, 30-059 Kraków, Poland, Poland

Received  July 2003 Revised  August 2004 Published  December 2004

We prove that the following properties are $C^0$ generic in the space of discrete dynamical systems on a compact smooth manifold $M$: periodic shadowing (Theorem 1.1) and, assuming dim$M\leq 3$, $\mathcal T_C$-inverse shadowing (Theorem 1.2).
Keywords: inverse) shadowing, (discrete) dynamical system, covering relations, handle decomposition, (periodic, Generic property.
Mathematics Subject Classification: Primary: 37C20, 37C50; Secondary: 54H2.
Citation: Piotr Kościelniak, Marcin Mazur. On $C^0$ genericity of various shadowing properties. Discrete and Continuous Dynamical Systems, 2005, 12 (3) : 523-530. doi: 10.3934/dcds.2005.12.523
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