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On the essential hyperbolicity of sectional-Anosov flows


Authors: S. Bautista and C. A. Morales
Journal: Proc. Amer. Math. Soc. 144 (2016), 205-215
MSC (2010): Primary 37D30, 37D45
DOI: https://doi.org/10.1090/proc/12686
Published electronically: June 24, 2015
MathSciNet review: 3415589
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Abstract: We prove that every sectional-Anosov flow of a compact $ 3$-manifold $ M$ exhibits a finite collection of hyperbolic attractors and singularities whose basins form a dense subset of $ M$. Applications include a characterization of essential hyperbolicity, sensitivity to the initial conditions and a relationship between the topology of $ M$ and the denseness of the basin of the singularities.


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Additional Information

S. Bautista
Affiliation: Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia
Email: sbautistad@unal.edu.co

C. A. Morales
Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530, 21945-970 Rio de Janeiro, Brazil
Email: morales@impa.br

DOI: https://doi.org/10.1090/proc/12686
Keywords: Anosov flow, sectional-Anosov flow, sensitive, essentially hyperbolic, $3$-manifold
Received by editor(s): December 18, 2013
Received by editor(s) in revised form: December 1, 2014
Published electronically: June 24, 2015
Additional Notes: The first author was partially supported by the Universidad Nacional de Colombia, Bogotá, Colombia
The second author was partially supported by CNPq, FAPERJ and PRONEX/Dynam. Sys. from Brazil and the Universidad Nacional de Colombia from Colombia. He would like to thank the Universidad Nacional de Colombia, Bogotá, Colombia, for its kind hospitality during the preparation of this paper.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2015 American Mathematical Society