Dynamics forced by homoclinic orbits

Valentín Mendoza

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arXiv · 1412.2737

Dynamics forced by homoclinic orbits

Valentín Mendoza

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Abstract

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.

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Valentín Mendoza. 2014-12-08. Dynamics forced by homoclinic orbits. https://arxiv.org/abs/1412.2737

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