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Quasi-Shadowing and Quasi-Stability for Dynamically Coherent Partially Hyperbolic Diffeomorphisms (1405.0081v1)
Published 1 May 2014 in math.DS
Abstract: Let $f$ be a partially hyperbolic diffeomorphism. $f$ is called has the quasi-shadowing property if for any pseudo orbit ${x_k}{k\in \mathbb{Z}}$, there is a sequence ${y_k}{k\in \mathbb{Z}}$ tracing it in which $y_{k+1}$ lies in the local center leaf of $f(y_k)$ for any $k\in \mathbb{Z}$. $f$ is called topologically quasi-stable if for any homeomorphism $g$ $C0$-close to $f$, there exist a continuous map $\pi$ and a motion $\tau$ along the center foliation such that $\pi\circ g=\tau\circ f\circ\pi$. In this paper we prove that if $f$ is dynamically coherent then it has quasi-shadowing and topological quasi-stability properties.