Pseudo-orbit shadowing in the C^1 topology

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2007, 17(2): 223-245. doi: 10.3934/dcds.2007.17.223

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, Brazil, Brazil

Received December 2005 Revised September 2006 Published November 2006

Abstract
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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).

Keywords: Heterodimensional cycle, Periodic point, Transitivity., Index, Pseudo-orbit Shadowing, Homoclinic class.

Mathematics Subject Classification: Primary: 37C20, 37C25; Secondary: 37D3.

Citation: Flavio Abdenur, Lorenzo J. Díaz. Pseudo-orbit shadowing in the $C^1$ topology. Discrete & Continuous Dynamical Systems - A, 2007, 17 (2) : 223-245. doi: 10.3934/dcds.2007.17.223

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