No-shadowing for singular hyperbolic sets with a singularity

2020/03/11 by Xiao Wen, Wen, Xiao, Lan Wen +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2003.05165

openalex publication_date 2020/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every singular hyperbolic chain transitive set with a singularity does not admit the shadowing property. Using this result we show that if a star flow has the shadowing property on its chain recurrent set then it satisfies Axiom A and the no-cycle conditions; and that if a multisingular hyperbolic set has the shadowing property then it is hyperbolic.

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