Pseudo-orbit shadowing in the $C^1$ topology

Flavio Abdenur; Lorenzo J. Díaz

doi:10.3934/dcds.2007.17.223

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2007, Volume 17, Issue 2: 223-245. Doi: 10.3934/dcds.2007.17.223

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Pseudo-orbit shadowing in the $C^1$ topology

Flavio Abdenur^1, and
Lorenzo J. Díaz^1,

1.
Dep. Matemática PUC-Rio, Marquês de São Vicente 225 22453-900, Rio de Janeiro

Received: November 30, 2005

Revised: August 31, 2006

Published: April 2007

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Abstract

We prove that the shadowing property does not hold for diffeomorphisms in an open and dense subset of the set of $C^1$-robustly non-hyperbolic transitive diffeomorphisms (i.e., diffeomorphisms with a $C^1$-neighborhood consisting of non-hyperbolic transitive diffeomorphisms).

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Mathematics Subject Classification: Primary: 37C20, 37C25; Secondary: 37D30.

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