arXiv subjects

H. M. Sánchez

Publications and source records attributed to H. M. Sánchez.

3 recordsLinked to original sources

arXiv2017

Intransitive sectional-Anosov flows on 3-manifolds

For each $n\in\mathbb{Z}^+$, we show the existence of Venice masks (i.e. intransitive sectional-Anosov flows with dense periodic orbits) 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.

math.DS↗

arXiv2017

On the intersection of homoclinic classes in intransitive sectional-Anosov flows

We show that if X is a Venice mask (i.e. nontransitive sectional-Anosov flow with dense periodic orbits) 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.

math.DS↗

arXiv2015

Sectional Anosov flows: Existence of Venice masks with two singularities

We show the existence of Venice masks (i.e. nontransitive sectional Anosov flows with dense periodic orbits), containing two equilibria on certain compact 3-manifolds. Indeed, the only known examples of venice masks have one or three singularities, and they are characterized by having two properties: are the union non disjoint of two homoclinic classes and whose intersection is the closure of the unstable manifold of a singularity. Thus, we present two type of examples containing two equilibria in which the homoclinic classes composing their maximal invariant set intersect in a very different way.

math.DS↗