arXiv subjects

Valentín Mendoza

Publications and source records attributed to Valentín Mendoza.

3 recordsLinked to original sources

arXiv2019

Dynamics forced by homoclinic orbits

The complexity of a dynamical system exhibiting a homoclinic orbit is given by the orbits that it forces. In this work we present a method, based in pruning theory, to determine the dynamical core of a homoclinic orbit of a Smale diffeomorphism on the 2-disk. Due to Cantwell and Conlon, this set is uniquely determined in the isotopy class of the orbit, up a topological conjugacy, so it contains the dynamics forced by the homoclinic orbit. Moreover we apply the method for finding the orbits forced by certain infinite families of homoclinic horseshoe orbits and propose its generalization to an arbitrary Smale map.

math.DS↗

arXiv2014

Renormalization and forcing of horseshoe orbits

In this paper we deal with the Boyland order of horseshoe orbits. We prove that there exists a set $\mathcal{R}$ of renormalizable horseshoe orbits containing only quasi-one-dimensional ones, that is, for these orbits the Boyland order coincides with the unimodal order.

math.DS↗

arXiv2012

Proof of the Pruning Front Conjecture for certain Hénon parameters

The Pruning Front Conjecture is proved for an open set of Hénon parameters far from unimodal. More specifically, for an open subset of Hénon parameter space, consisting of two connected components one of which intersects the area-preserving locus, it is shown that the associated Hénon maps are prunings of the horseshoe. In particular, their dynamics is a subshift of the two-sided two-shift.

math.DS↗