EVENT DETAILS AND ABSTRACT

Title: Fuchsian groups and generalized Bowen-Series maps
Speaker: Ilie Ugarcovici
Speaker Info: DePaul University
Brief Description:
Special Note:
Abstract:

Bowen and Series (1979) constructed a Markov map on the unit circle that is orbit equivalent to the action of a given co-finite Fuchsian group. Such a construction relies on a well chosen fundamental domain of the Fuchsian group (in the Poincaré disk model) and a partition of the boundary circle by the endpoints of the isometric circles of the group generators. We investigate a generalized version of this type of maps associated to arbitrary partitions of the boundary circle. We show how several dynamical properties can be obtained from some geometric considerations about the two-dimensional extensions of these circle maps. This is joint work with S. Katok (Penn State).