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On the genericity of the shadowing property for conservative homeomorphisms
Pierre-Antoine Guihéneuf, Thibault Lefeuvre
Source 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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