Speaker: Dzmitry Dudko, Stony Brook University
January 8, 2024 02:30 PM
- 03:30 PM
Abstract:
In the parameter space of rational maps, we consider hyperbolic components of the disjoint type: all critical points are simple and attracted by different periodic cycles. With extra markings, such hyperbolic components are open polydisks parametrized by multipliers of attracting cycles. We will show that if the Julia set is a Sierpinski carpet, then the hyperbolic component is bounded, and its closure is a closed polydisk; i.e., no obstructions at the boundary. For boundaries of non-Sierpinski components, we introduce a Thurston-type realization criterion: the set of obstructed maps of the "regular'' kind (no "doubly-parabolic" collisions) is the closure of the set of geometrically finite obstructed maps. We will also mention dynamical consequences.
Joint work with Yusheng Luo.