Event Type:

Department Colloquium

Date/Time:

Monday, October 13, 2008 - 09:00

Location:

Kidder 364

Guest Speaker:

Institution:

Institut de Mathematiques de Luminy, Marseille France

Abstract:

An interval exchange transformation is given by partitioning the unit interval into a union of n subintervals and rearranging the subintervals by translations according to some permutation of n letters. Iterating this process gives a dynamical system. Interval exchange transformations were introduced by the Russian school in the 1960s, interest in them was revived by Keane in the 1970s and exploded with Thurston's work. When n=2, one can view the interval exchange as a circle rotation, and there is a direct connection between the symbolic dynamics of the interval exchange and the continued fraction expansion of the rotation angle. We extend this connection to larger values of n by giving a complete word-combinatorial characterization of those symbolic sequences which arise as natural codings of interval exchange transformations, and in some cases build them explicitly through a new induction process, giving new insight on the dynamics of these transformations.