[Binghamton Geometry/Topology Seminar] Nov 3

[Dmytro Savchuk]

Also, please note, that there will be a colloquium talk after the seminar
talk by Anatole Katok that is of interest to topology people:
http://www.math.binghamton.edu/dept/colloquia/index.html

                   BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

*Date:*  Thursday, Nov 3, 2011

*Time:*  2:50-3:50pm
*Place:*  Library North 2205 followed by coffee/tea in the Anderson Reading
Room.

*Speaker:* Svetlana Katok* *(Penn State)
*Title: *Reduction theory, coding of geodesics, and continued fractions
*
Abstract:*  I will discuss a method of coding of geodesics on surfaces of
constant negative curvature using boundary maps and "reduction theory".
For compact surfaces these maps are generalizations of the Bowen-Series
map. For the modular surface they are related to a family of
(a,b)-continued fractions. In special cases, when an (a,b)-expansion has a
so-called "dual", the coding sequences are obtained by juxtaposition of
the boundary expansions of the fixed points, and the set of coding
sequences is a countable sofic shift. I will also give a dynamical
interpretation of the ”reduction theory” which underlines these
constructions and its relation to the attractor of a certain associated
natural extension map. The talk is based on joint works with Ilie
Ugarcovici.
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