USNA Mathematics Department seminar

The talks for the academic year 1997-98 are held in Chauvenet 116 at 3:45 pm unless otherwise stated.

 

 

Speaker:

Tom Fitzkee


George Washington Univ.

 

Title:

Weakly mixing tiling flows arising from interval exchange transformations

 

 

Abstract: We give an explicit example of a pseudo-Anosov diffeomorphism D on a surface M of genus 2 such that the expansion coefficient theta is not a Pisot number. Considering the unit speed flow Ft along the nonsingular leaves of the expanding foliation, Ft is minimal, uniquely ergodic (for the surface area) and weakly, but not strongly, mixing. Constructing a Markov partition P for D on M, the sets in P induce tilings of R on the orbits of Ft. The corresponding tiling dynamical system is, then, an almost 1:1 extension of Ft, satisfying an inflation map induced by the diffeomorphism D. This provides an example of a weakly mixing tiling dynamical system which has a ``smooth model".

 

 

Time: Wednesday, February 4

 

 

Reception at 3:30 in the common room on the 3rd floor of Chauvenet Hall.