“Asymptotic Counting in Conformal Dynamical Systems”
Speaker: Mariusz Urbański, University of North Texas
Abstract: I will consider the general setting of conformal graph directed Markov systems modeled by countable state symbolic subshifts of finite type. I will talk about two classes of such systems: attracting and parabolic. The latter being treated by means of the former. I will provide fairly complete asymptotic counting results for multipliers and diameters associated with preimages or periodic orbits ordered by a natural geometric weighting. These results will have direct applications to a wide variety of examples, including the case of Apollonian Circle Packings, Apollonian Triangle, expanding and parabolic rational functions, Farey maps, continued fractions, Mannenville-Pomeau maps, Schottky groups, Fuchsian groups. Our approach is founded on spectral properties of complexified Ruelle--Perron--Frobenius operators and Tauberian theorems as used in classical problems of prime number theory.
Room Reservation Information
Room Number: 114 McAllister
Time: 2:30pm - 3:30pm