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Dynamical Systems seminar - David homeomorphisms and applications in mating and removability

Dates
Wednesday, May 12, 2021 - 13:00 to 14:00

Speaker: Dimitrios Ntalampekos (Stony Brook University)


Abstract: The main object in this talk will be the mating of piecewise (anti-)analytic dynamical systems of the unit disk. While quasiconformal maps can be used for the mating of two hyperbolic dynamical systems, they are insufficient for mating a hyperbolic dynamical system with a parabolic one. Instead, we achieve the mating using the notion of a David homeomorphism, which is a generalization of a quasiconformal homeomorphism that allows unbounded quasiconformal dilatation. The main theorem that we will discuss provides extensions of a general class of dynamically defined circle homeomorphisms to David homeomorphisms of the unit disk. An implication of this theory is that limit sets of a certain class of Kleinian reflection groups (called necklace reflection groups) are conformally removable. The talk is based on joint work with Misha Lyubich, Sergei Merenkov, Sabyasachi Mukherjee, and Christina Karafyllia.