Videos

Conformal Dynamics, 2

January 21, 2015
Keywords:
  • conformal geometry
  • complex dynamics
  • orbits
  • quasi-circle
  • cocompactness
  • ergodic measure
MSC:
  • 37A20
  • 37A25
  • 37Axx
  • 37-xx
  • 37Fxx
  • 37F99
Abstract
This minicourse is an introduction to the group of conformal transformations of the sphere. We will focus on its action on the space of non-singleton compact subsets of the sphere. 1. Conformal autosimilarity: we will see that the compact subsets whose orbit is closed are exactly the limit sets of convex cocompact subgroups. 2. Quasicircles: we will see that the compact subsets whose orbit closure contains only Jordan curves are exactly the quasicircles. 3. Minimal orbits: we will construct compact subsets of the sphere whose orbit is not closed but whose orbit closure is minimal.