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Explosion of differentiability for equivalencies between Anosov flows on $ 3$-manifolds


Authors: Mário Bessa, Sérgio Dias and Alberto A. Pinto
Journal: Proc. Amer. Math. Soc. 144 (2016), 3757-3766
MSC (2010): Primary 37D20, 37C15; Secondary 37D10
DOI: https://doi.org/10.1090/proc/12977
Published electronically: May 4, 2016
MathSciNet review: 3513536
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Abstract: For Anosov flows obtained by suspensions of Anosov diffeomorphisms on surfaces, we show the following type of rigidity result: if a topological conjugacy between them is differentiable at a point, then the conjugacy has a smooth extension to the suspended $ 3$-manifold. This result generalizes the similar ones of Sullivan and Ferreira-Pinto for 1-dimensional expanding dynamics and also a result of Ferreira-Pinto for 2-dimensional hyperbolic dynamics.


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Additional Information

Mário Bessa
Affiliation: CMA-UBI, Departamento de Matemática da Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6201-001 Covilhã, Portugal
Email: bessa@ubi.pt

Sérgio Dias
Affiliation: Departamento de Matemática, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal
Email: sergiodias@fc.up.pt

Alberto A. Pinto
Affiliation: LIAAD-INESC TEC, Departmamento de Matemática, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal
Email: aapinto@fc.up.pt

DOI: https://doi.org/10.1090/proc/12977
Keywords: Anosov flow, topological and differentiable equivalence, conjugacy.
Received by editor(s): December 26, 2014
Received by editor(s) in revised form: September 24, 2015
Published electronically: May 4, 2016
Additional Notes: The first author was supported in part by National Funds through FCT - “Fundação para a Ciência e a Tecnologia” (Portuguese Foundation for Science and Technology), project PEst-OE/MAT/UI0212/2011.
The third author acknowledges the financial support of LIAAD-INESC TEC through program PEst, USP-UP project, Faculty of Sciences, University of Porto, Calouste Gulbenkian Foundation, the financial support received by the FCT – Fundação para a Ciência e a Tecnologia within project UID/EEA/50014/2013 and ERDF (European Regional Development Fund) through the COMPETE Program (operational program for competitiveness) and by National Funds through the FCT within Project “Dynamics, optimization and modelling”, with reference PTDC/MAT-NAN/6890/2014, and the financial support received through the CNPq Special Visiting Researcher scholarship program “Dynamics, Games and Applications”, with reference 401068/2014-5, at IMPA, Brazil 401068/2014-5 - Título : Dinâmica, Jogos e Aplicações.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2016 American Mathematical Society

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