Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 13.12.2011 |
| Speaker: | Vincent Delecroix, Université Paris VII |
| Title: | Divergent trajectories in a periodic billiard in the plane |
| Abstract: | We study the periodic windtree model: a particule moves in the plane (``the wind'') and collides with the usual law of geometric optic on periodically placed rectangles of the same size (``the trees''). Using an induction procedure of S. Ferenczi and L. Zamboni we build cutting sequences associated to the trajectories and prove that there exist many parameters (size of the rectangles and initial direction) for which the trajectory is divergent: the trajectory eventually leaves any compact. The result holds independently of the departure point! |
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