Partial hyperbolicity and central shadowing

Sergey Kryzhevich; Sergey Tikhomirov

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arXiv · 1112.4272

Partial hyperbolicity and central shadowing

Sergey Kryzhevich·Sergey Tikhomirov

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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.

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Sergey Kryzhevich, Sergey Tikhomirov. 2012-02-11. Partial hyperbolicity and central shadowing. https://arxiv.org/abs/1112.4272

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