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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the essential hyperbolicity of sectional-Anosov flows
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by S. Bautista and C. A. Morales PDF
Proc. Amer. Math. Soc. 144 (2016), 205-215 Request permission

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
  • MR Author ID: 643938
  • 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
  • MR Author ID: 611238
  • ORCID: 0000-0002-4808-6902
  • Email: morales@impa.br
  • 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
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 205-215
  • MSC (2010): Primary 37D30, 37D45
  • DOI: https://doi.org/10.1090/proc/12686
  • MathSciNet review: 3415589