Intransitive Sectional-Anosov Flows on 3-manifolds

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; Lopez Barragan and Sanchez in Bull Braz Math Soc N Ser 48(1): 1–18, 2017, Morales and Pacifico 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.