For more information about this meeting, contact Anatole Katok, Diane Henderson, Svetlana Katok.
|Title:||Coding in dynamics and geometry, I.|
|Seminar:||Working Seminar: Dynamics and its Working Tools|
|We start with some basic information about the hyperbolic plane: the group of orientation preserving transformations, unit tangent bundle, their identification, geodesic flow. Then I will define the modular group and modular surface and explain about some general properties of geodesics on the surface. The second part of the introduction is dedicated to symbolic dynamics in general: Bernoulli shift, subshifts of finite type, k-step Markov chains.
The main part of the talk will be about different codings of geodesics on the modular surface. Arithmetic codes: Gauss's, Artin's and Hurwitz's codes, continued fractions associated with them. General (a,b)-continued fractions and codes emerging from those. Geometric (Morse's) code: in general and on the modular surface.|
Room Reservation Information
|Date:||01 / 22 / 2008|
|Time:||03:30pm - 06:00pm|