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Sectional Anosov Flows: Existence of Venice Masks with Two Singularities

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Abstract

We show the existence of Venice masks (i.e. nontransitive sectional Anosov flows with dense periodic orbits, Bautista and Morales http://preprint.impa.br/Shadows/SERIE_D/2011/86.html; Bautista et al. Discr Contin Dyn Syst 19(4):761, 2007; Morales and Pacífico Pac J Math 216(2):327–342, 2004, Morales et al. Pac J Math 229(1):223–232, 2007) containing two equilibria on certain compact 3-manifolds. Indeed, we present two type of examples in which the homoclinic classes composing their maximal invariant set intersect in a very different way.

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Authors and Affiliations

  1. Departamento de Matemática, Instituto de Ciências Exatas (ICE), Universidade Federal Rural do Rio de Janeiro, Seropédica, Brazil

    Andrés M. López Barragán

  2. Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

    Henry M. S. Sánchez

Authors
  1. Andrés M. López Barragán
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  2. Henry M. S. Sánchez
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Correspondence to Andrés M. López Barragán.

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This work was partially supported by CAPES, Brazil.

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Barragán, A.M.L., Sánchez, H.M.S. Sectional Anosov Flows: Existence of Venice Masks with Two Singularities. Bull Braz Math Soc, New Series 48, 1–18 (2017). https://doi.org/10.1007/s00574-016-0015-7

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  • DOI: https://doi.org/10.1007/s00574-016-0015-7

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