Homoclinic spirals

Homoclinic spirals - Eran Igra (Technion)

Homoclinic trajectories are long known as a theoretical scenario leading to chaos. In this talk we will review the basics of homoclinic bifurcations and how they can perturb a relatively “well-behaved” system into chaos. We will begin with the Shilnikov scenario, after which we will consider Belyakov’s theorem, and show its application to the analysis of some famous three-dimensional flows. Time permitting, we will review how homoclinic bifurcations lead to the appearance of spirals in the parameter plane, and how this setting implies analogous results to Feigenbaum universality for three-dimensional flows.