Average Elliptic Billiard Invariants with Spatial Integrals
Dynamical Systems
2021-02-23 v1 Systems and Control
Systems and Control
Abstract
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.
Keywords
Cite
@article{arxiv.2102.10899,
title = {Average Elliptic Billiard Invariants with Spatial Integrals},
author = {Jair Koiller and Dan Reznik and Ronaldo Garcia},
journal= {arXiv preprint arXiv:2102.10899},
year = {2021}
}
Comments
9 pages, 6 figures