Jonathan Fraser

Orbital sets in conformal dynamics

Given a (non-dynamically defined) set E and some dynamics acting on the ambient space, the orbital set is simply the appropriately defined orbit of E under the dynamics. The orbital set then shares (fractal) features of E and the attractor/repeller of the dynamical system. I am interested in questions where the answer depends on both objects, such as 'what is the box dimension of the orbital set?' I will discuss concrete examples of this idea in two settings: Kleinian group actions on hyperbolic space and rational maps acting on the complex plane. This is based on joint work with Tom Bartlett and Yunlong Xu.