Partial hyperbolicity and central shadowing

Sergey Kryzhevich; Sergey Tikhomirov

doi:10.3934/dcds.2013.33.2901

Article Contents

2013, Volume 33, Issue 7: 2901-2909. Doi: 10.3934/dcds.2013.33.2901

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Partial hyperbolicity and central shadowing

Sergey Kryzhevich^1, and
Sergey Tikhomirov^2,

1.
Faculty of Mathematics and Mechanics and Chebyshev laboratory, Saint-Petersburg State University Universitetsky pr., 28, 198504, Peterhof, St. Petersburg
2.
Institut fur Mathematik, Freie Universitat Berlin, Arnimallee 3, Berlin, 14195

Received: February 29, 2012

Revised: October 31, 2012

Published: June 2013

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Abstract

We study shadowing property for a partially hyperbolic diffeomorphism $f$. It is proved that if $f$ is dynamically coherent then any pseudotrajectory can be shadowed by a pseudotrajectory with ``jumps'' along the central foliation. The proof is based on the Tikhonov-Shauder fixed point theorem.

Keywords:

Mathematics Subject Classification: 37C50, 37D30.

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