Quasi-Shadowing and Quasi-Stability for Dynamically Coherent Partially Hyperbolic Diffeomorphisms

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 $g$ $C^0$-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.

11 pages, 1 figure

Cited by in corpus (2)

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