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

2014/05/01 by Huyi Hu, Yunhua Zhou, Hu, Huyi +3 · 1 citation
Mathematics · Physics and Astronomy · #37C15 #37C50 #37D30 #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:37C15 #msc:37C50 #msc:37D30

paper · pdf · doi:10.48550/arxiv.1405.0081

11 pages, 1 figure

arxiv created 2014/05/01 · openalex publication_date 2014/05/01 · arxiv updated 2014/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f be a partially hyperbolic diffeomorphism. f is called has the quasi-shadowing property if for any pseudo orbit \x_k\_{k∈ ℤ}, there is a sequence \y_k\_{k∈ ℤ} tracing it in which y_k+1 lies in the local center leaf of f(y_k) for any k∈ ℤ. f is called topologically quasi-stable if for any homeomorphism g C⁰-close to f, there exist a continuous map π and a motion τ along the center foliation such that π∘ g=τ∘ f∘π. In this paper we prove that if f is dynamically coherent then it has quasi-shadowing and topological quasi-stability properties.

Citations

• On the Plaque Expansivity Conjecture

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• Subsystems with shadowing property for ℤ^k-actions

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