Product Anosov diffeomorphisms and the two-sided limit shadowing property
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Abstract:
We characterize product Anosov diffeomorphisms in terms of the two-sided limit shadowing property. It is proved that an Anosov diffeomorphism is a product Anosov diffeomorphism if and only if any lift to the universal covering has the unique two-sided limit shadowing property. Then we introduce two maps in a suitable Banach space such that fixed points of these maps are related with shadowing orbits on the universal covering.References
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Additional Information
- Bernardo Carvalho
- Affiliation: Departamento de Matematica, Universidade Federal de Minas Gerais - UFMG, Belo Horizonte MG, Brazil
- MR Author ID: 1027591
- ORCID: 0000-0002-9400-0882
- Email: bmcarvalho06@gmail.com
- Received by editor(s): May 1, 2016
- Received by editor(s) in revised form: February 27, 2017, and April 18, 2017
- Published electronically: September 13, 2017
- Communicated by: Yingfei Yi
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 1151-1164
- MSC (2010): Primary 37D20; Secondary 37C20
- DOI: https://doi.org/10.1090/proc/13790
- MathSciNet review: 3750227