2019/06/10 by Anani Komla Adabrah, Adabrah, Anani Komla, Vladimir Dragović +3
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Quantum chaos and dynamical systems #Scientific Research and Discoveries
paper · pdf · doi:10.48550/arxiv.1906.04911
openalex publication_date 2019/06/10 · openalex created_date 2022/07/22 · openalex updated_date 2026/07/28
We derive necessary and sufficient conditions for periodic and for elliptic\nperiodic trajectories of billiards within an ellipse in the Minkowski plane in\nterms of an underlining elliptic curve. We provide several examples of periodic\nand elliptic periodic trajectories with small periods. We observe relationship\nbetween Cayley-type conditions and discriminantly separable and factorizable\npolynomials. Equivalent conditions for periodicity and elliptic periodicity are\nderived in terms of polynomial-functional equations as well. The corresponding\npolynomials are related to the classical extremal polynomials. In particular,\nthe light-like periodic trajectories are related to the classical Chebyshev\npolynomials. The similarities and differences with respect to previously\nstudied Euclidean case are indicated.\n