Intransitive Sectional-Anosov Flows on 3-manifolds

• Bautista, S ^[1] ; López, A M ^[2] ; Sánchez, H M ^[3]
  1. [1] Universidad Nacional de Colombia

     Universidad Nacional de Colombia

     Colombia

     
  2. [2] Universidade Federal Rural do Rio de Janeiro

     Universidade Federal Rural do Rio de Janeiro

     Brasil

     
  3. [3] Universidad Central

     Universidad Central

     Hospital, Costa Rica

     

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 18, Nº 2, 2019, págs. 615-630
• Idioma: inglés
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  • For each n∈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.