On C^0 genericity of various shadowing properties

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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

Abstract
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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 & Continuous Dynamical Systems - A, 2005, 12 (3) : 523-530. doi: 10.3934/dcds.2005.12.523

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