PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Svetlana Katok, Stephanie Zerby, Anatole Katok, Federico Rodriguez Hertz.

Title:Combinatorics and entropy of continued fractions with SL(2, Z) branches
Seminar:Dynamical systems seminar
Speaker:Giulio Tiozzo, Yale University
Abstract:
As is well-known, the Gauss map generates the usual continued fraction algorithm and is related to the geodesic flow on the modular surface. We shall look at the dynamics of generalized Gauss maps whose branches are Moebius transformations in SL(2, Z). These maps, also known as (a, b)-continued fractions, have been introduced by S. Katok and I. Ugarcovici. We provide an explicit construction of the bifurcation locus for this family, and show it is parametrized by Farey words and combinatorially isomorphic to the main cardioid in the Mandelbrot set. As a consequence, we prove that the entropy is a monotone function of the parameter. This is joint work with C. Carminati and S. Isola.

Room Reservation Information

Room Number:MB114
Date:02 / 16 / 2015
Time:03:35pm - 04:35pm