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Intransitive Sectional-Anosov Flows on 3-manifolds

  • S. Bautista
  • A. M. López
  • H. M. Sánchez
Article
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Abstract

For each \(n\in \mathbb {Z}^+\), we show the existence of Venice masks (i.e. intransitive sectional-Anosov flows with dense periodic orbits, Bautista and Morales in Lectures on sectional-Anosov flows. http://preprint.impa.br/Shadows/SERIE_D/2011/86.html, 2011; Bautista and Morales in Discrete Contin Dyn Syst 19(4): 761–775, 2007; López Barragan and Sánchez in Bull Braz Math Soc N Ser 48(1): 1–18, 2017, Morales and Pacífico in Pac J Math 216(2): 327–342, 2004) containing n equilibria on certain compact 3-manifolds. These examples are characterized because of the maximal invariant set is a finite union of homoclinic classes. Here, the intersection between two different homoclinic classes is contained in the closure of the union of unstable manifolds of the singularities.

Keywords

Sectional Anosov flow Maximal invariant set Lorenz-like singularity Homoclinic class Venice mask Dense periodic orbits 

Notes

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Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad Nacional de ColombiaBogotáColombia
  2. 2.Departamento de Matemática, Instituto de Ciências Exatas (ICE)Universidade Federal Rural do Rio de JaneiroSeropédicaBrazil
  3. 3.Departamento de MatemáticasUniversidad CentralBogotáColombia

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