Oriented shadowing property and Ω-stability for vector fields

2014/04/14 by Shaobo Gan, Gan, Shaobo, Ming Li +4
Mathematics · #37C50 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS #msc:37C50

paper · pdf · doi:10.48550/arxiv.1404.3545

openalex publication_date 2014/04/14 · arxiv created 2014/08/11 · arxiv updated 2014/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We call that a vector field has the oriented shadowing property if for any ε>0 there is d>0 such that each d-pseudo orbit is ε-oriented shadowed by some real orbit. In this paper, we show that the C¹-interior of the set of vector fields with the oriented shadowing property is contained in the set of vector fields with the Ω-stability.

Citations

• On Various Types of Shadowing for Geometric Lorenz Flows

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• A note on shadowing properties
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