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

@article{Hu2014QuasiShadowingAQ, title={Quasi-Shadowing and Quasi-Stability for Dynamically Coherent Partially Hyperbolic Diffeomorphisms}, author={Huyi Hu and Yunhua Zhou and Yujun Zhu}, journal={arXiv: Dynamical Systems}, year={2014} }

Let f be a partially hyperbolic diffeomorphism. f is called has the quasi- shadowing property if for any pseudo orbit {xk}k∈Z, there is a sequence {yk}k∈Z tracing it in which yk+1 lies in the local center leaf of f(yk) for any k ∈ Z. f is called topologically quasi-stable if for any homeomorphism g C 0 -close to f, there exist a

## 5 Citations

### Quasi-shadowing Property on Random Partially Hyperbolic Sets

- MathematicsActa Mathematica Sinica, English Series
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In this paper we investigate the quasi-shadowing property for C1 random dynamical systems on their random partially hyperbolic sets. It is shown that for any pseudo orbit {xk}−∞+∞ on a random…

### SUBSYSTEMS WITH SHADOWING PROPERTY FOR Z-ACTIONS

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In this paper, subsystems with shadowing property for Z-actions are investigated. Let α be a continuous Z-action on a compact metric space X. We introduce the notions of pseudo orbit and shadowing…

### Center Specification Property and Entropy for Partially Hyperbolic Diffeomorphisms

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- 2015

Let $f$ be a partially hyperbolic diffeomorphism on a closed (i.e., compact and boundaryless) Riemannian manifold $M$ with a uniformly compact center foliation $\mathcal{W}^{c}$. The relationship…

### Subsystems with shadowing property for $\mathbb{Z}^{k}$-actions

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- 2021

In this paper, subsystems with shadowing property for Z-actions are investigated. Let α be a continuous Z-action on a compact metric space X. We introduce the notions of pseudo orbit and shadowing…

### Quasi-Shadowing for Partially Hyperbolic Flows with a Local Product Structure

- MathematicsJournal of Dynamical and Control Systems
- 2021

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