On the genericity of the shadowing property for conservative homeomorphisms

Guihéneuf, Pierre-Antoine; Lefeuvre, Thibault

doi:10.1090/proc/13526

On the genericity of the shadowing property for conservative homeomorphisms
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by Pierre-Antoine Guihéneuf and Thibault Lefeuvre PDF

Proc. Amer. Math. Soc. 146 (2018), 4225-4237 Request permission

Abstract:

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

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