Kirthana Rajasekar: Attractors and intermingled basins

This topic falls in the area of dynamical systems and ergodic theory. More specifically, we discuss dynamical systems of the form (X,T), where X is a topological space and T is a map on X. At its core, this area involves the study of the long-term behavior of trajectories in X and the underlying patterns that emerge. A natural pursuit has been to characterise the notion of stability for various dynamical systems. A significant part of this pursuit has been the study of attractors, which are compact sets in X to which "most" trajectories converge to. In this talk, we'll define an attractor and its basin of attraction, and discuss a few examples, to justify the necessity of defining them as such. The discussion will lead up to one cool example, demonstrating the case of multiple attractors with intermingled basins.