Dia: Dimecres 30 d'abril de 2025
Lloc: Aula T2 (segon pis), Facultat de Matemàtiques i Informàtica, UB.
A càrrec de: Rafael Ramírez, UPC
Títol: High-order persistence of resonant caustics in perturbed circular billiards
Resum: We find necessary and sufficient conditions for high-order persistence of resonant caustics in perturbed circular billiards. The main technical tool is a high-order perturbation theory based on the Bialy-Mironov generating function for convex billiards. A caustic is a curve such that any billiard trajectory, once tangent to the curve, stays tangent after every reflection. A convex caustic is p/q-resonant when all its tangent trajectories form closed polygons with q sides that make p turns around the caustic.
We prove that any resonant caustic of the circular billiard with period q persist up to order ⌈ q/n ⌉ -1 under any polynomial perturbation of degree n of the circle.
Join work with Comlan Edmond Koudjinan @ University of Toronto.
Last updated: Fri Apr 25 14:21:22 2025