A study on the generation of chaos due to the presence of smale horseshoes in dynamical systems with a homoclinic orbit

Abstract

One of the fundamental problems in dynamical systems is the detection and characterisation of chaotic behaviours. In this work we will focus on chaos induced by what is called the Smale horseshoe. Smale horseshoes frequently appear, but not exclusively, in the hyperbolic context and in what is known as the Sil'nikov Phenomenon. We will also present a generalization of the described phenomenons to systems with parabolic points.