Average Elliptic Billiard Invariants with Spatial Integrals

Autor:	Koiller, Jair, Reznik, Dan, Garcia, Ronaldo
Rok vydání:	2021
Předmět:	Mathematics - Dynamical Systems Electrical Engineering and Systems Science - Systems and Control 37-40 51N20 51M04 51-04
Druh dokumentu:	Working Paper
Popis:	We compare invariants of N-periodic trajectories in the elliptic billiard, classic and new, to their aperiodic counterparts via a spatial integrals evaluated over the boundary of the elliptic billiard. The integrand is weighed by a universal measure equal to the density of rays hitting a given boundary point. We find that aperiodic averages are smooth and monotonic on caustic eccentricity, and perfectly match N-periodic average invariants at the discrete caustic parameters which admit a given N-periodic family. Comment: 9 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2102.10899 Zobrazit plný text záznamu View this record from Arxiv