On the genericity of the shadowing property for conservative\n homeomorphisms

2016/06/09 by Pierre‐Antoine Guihéneuf, Guihéneuf, Pierre-Antoine, Thibault Lefeuvre +1
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.1606.02924

Abstract

We prove the genericity of the shadowing and periodic shadowing properties\nfor both conservative and dissipative homeomorphisms on a compact connected\nmanifold. Our proof is valid for topological manifolds and still holds in the\ndissipative case. As a consequence of this result, we establish the genericity\nof the specification property, the average shadowing property and the\nasymptotic average shadowing property in the conservative case.\n

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