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Product Anosov diffeomorphisms and the two-sided limit shadowing property


Author: Bernardo Carvalho
Journal: Proc. Amer. Math. Soc. 146 (2018), 1151-1164
MSC (2010): Primary 37D20; Secondary 37C20
DOI: https://doi.org/10.1090/proc/13790
Published electronically: September 13, 2017
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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.


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Additional Information

Bernardo Carvalho
Affiliation: Departamento de Matematica, Universidade Federal de Minas Gerais - UFMG, Belo Horizonte MG, Brazil
Email: bmcarvalho06@gmail.com

DOI: https://doi.org/10.1090/proc/13790
Keywords: Anosov, hyperbolicity, transitivity.
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
Article copyright: © Copyright 2017 American Mathematical Society

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