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.

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We show that if X is a Venice mask (i.e. nontransitive sectional-Anosov flow with dense periodic orbits, [9], [25], [24], [18]) supported on a compact 3-manifold, then the omega-limit set of every non-recurrent point in the unstable manifold of some singularity is a closed orbit. In addition, we prove that the intersection of two different homoclinic classes in the maximal invariant set of a sectional-Anosov flow can be decomposed as the disjoint union of, singular points, a non-singular hyperbolic set, and regular points whose alpha-limit set and omega-limit set is formed by singular points or hyperbolic sets.

We show the existence of venice masks (i.e. nontransitive sectional Anosov flows with dense periodic orbits, [3], [8], [9],[2]) 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.