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Asymptotic orbital shadowing property for diffeomorphisms
- Source :
- Open Mathematics, Vol 17, Iss 1, Pp 191-201 (2019)
- Publication Year :
- 2019
- Publisher :
- De Gruyter, 2019.
-
Abstract
- Let M be a closed smooth Riemannian manifold and let f : M → M be a diffeomorphism. We show that if f has the C1 robustly asymptotic orbital shadowing property then it is an Anosov diffeomorphism. Moreover, for a C1 generic diffeomorphism f, if f has the asymptotic orbital shadowing property then it is a transitive Anosov diffeomorphism. In particular, we apply our results to volume-preserving diffeomorphisms.
Details
- Language :
- English
- ISSN :
- 23915455
- Volume :
- 17
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Open Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.30be1752e9e42d9953403a6151ddabb
- Document Type :
- article
- Full Text :
- https://doi.org/10.1515/math-2019-0002