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arXiv · 1606.02924

On the genericity of the shadowing property for conservative homeomorphisms

Pierre-Antoine Guihéneuf·Thibault Lefeuvre
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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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Pierre-Antoine Guihéneuf, Thibault Lefeuvre. 2016-07-26. On the genericity of the shadowing property for conservative homeomorphisms. https://arxiv.org/abs/1606.02924

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