Comparison between attractors in skew product dynamical systems with attractors in dynamical systems

Abstract

In this paper, we compare a skew product dynamical system with the general dynamical system, in terms of attraction for both systems. More specifically, we investigate the notions of attractor, basin of attraction, compactness and invariance of the attractor. We also give an example of skew product map where the map exhibit an invariant graph (i.e. attractor). From this project, we observe that by using the skew product system, we are able to study the attraction of the orbits to the attractor in more systematic way where instead of attracting from all directions in the metric space, they converge in fibre directions such that the orbits move vertically closer and closer along the fibres until they intercept with the attractor, or namely the invariant graph.