On the genericity of the shadowing property for conservative homeomorphisms
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- by Pierre-Antoine Guihéneuf and Thibault Lefeuvre PDF
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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.References
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Additional Information
- Pierre-Antoine Guihéneuf
- Affiliation: Universidade Federal Fluminense, Rua Mário Santos Braga, 24020-140, Niterói, RJ, Brasil
- Address at time of publication: IMJ-PRG, 4 Place Jussieu, case 247, 75252 Paris Cedex 05, France
- MR Author ID: 985450
- Email: pguiheneuf@id.uff.br
- Thibault Lefeuvre
- Affiliation: École Polytechnique, Route de Saclay, 91128 Palaiseau, France
- Address at time of publication: Laboratoire de Mathématiques d’Orsay, Univ Paris-Sud, CNRS, Université Pans Saclay, 91405, Orsay, France
- Email: thibault.lefeuvre@u-psud.fr
- Received by editor(s): June 6, 2016
- Received by editor(s) in revised form: July 26, 2016, and September 12, 2016
- Published electronically: June 28, 2018
- Additional Notes: The first author was funded by an IMPA/CAPES grant.
- Communicated by: Yingfei Yi
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 4225-4237
- MSC (2010): Primary 37B05
- DOI: https://doi.org/10.1090/proc/13526
- MathSciNet review: 3834653