On $C^0$ genericity of various shadowing properties

Piotr Kościelniak; Marcin Mazur

doi:10.3934/dcds.2005.12.523

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2005, Volume 12, Issue 3: 523-530. Doi: 10.3934/dcds.2005.12.523

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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

Received: June 30, 2003

Revised: July 31, 2004

Published: March 2005

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Abstract

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).

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Mathematics Subject Classification: Primary: 37C20, 37C50; Secondary: 54H20.

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