Uniqueness of billiards coding in polygon
Date/Time:10 Apr 2019 14:00
Venue: S17 #05-11 SR5
Speaker: Li Yunzhe, National University of Singapore
Uniqueness of billiards coding in polygon
The study of mathematical billiards is a rich subject in dynamical systems. It describes the frictionless motion of a mass point in a domain with elastic reflection on the boundary. Among many other variations of mathematical billiards, polygonal billiards concerns the billiard problem in a two dimensional polygonal domain. One particular strategy to study polygonal billiards is to encode the trajectory of a billiard by the sequence of sides of the polygonal domain hit by the billiard along its trajectory. Several questions could be asked regarding this encoding and its relations with the billiard. Especially, we may want to know to what extend this encoding determines the physical trajectory of the billiard in the polygonal domain? In 1993, it has been proven by G. Galperin, T. Krüger and S. Troubetzkoy that for a non periodic trajectory in a simply connected polygon the encoding uniquely determines the physical trajectory. We aims to generalise this result to a wider class of polygons which are not necessarily simply connected but contain a finite number of holes such that the holes have non zero minimal diameter.
This result was proven in a research project in 2018 at Aix-Marseille université under the supervision of S. Troubetzkoy.
Add to calendar: 
