2021/02/22 by Jair Koiller, Koiller, Jair, Dan Reznik +3
Mathematics · Physics and Astronomy · #37-40 #51-04 #51M04 #51N20 #Black Holes and Theoretical Physics #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2102.10899
openalex publication_date 2021/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.