Intransitive Sectional-Anosov Flows on 3-manifolds

Abstract

For each n ∈ Z + , we show the existence of Venice masks (i.e. intransitive sectional-Anosov flows with dense periodic orbits, [6], [18], [4], [13]) 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. * Key words and phrases: Sectional Anosov flow, Maximal invariant set, Lorenz-like singularity, Homoclinic class, Venice mask, Dense periodic orbits. This work is partially supported by CAPES, Brazil.