2020/11/12 by Ronaldo Garcia, Garcia, Ronaldo, Dan Reznik +1
Physics and Astronomy · Mathematics · Materials Science · #Quantum chaos and dynamical systems #Geometric and Algebraic Topology #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.2011.06640
We study self-intersected N-periodics in the elliptic billiard, describing new facts about their geometry (e.g., self-intersected 4-periodics have vertices concyclic with the foci). We also check if some invariants listed in "Eighty New Invariants of N-Periodics in the Elliptic Billiard" (2020), arXiv:2004.12497, remain invariant in the self-intersected case. Toward that end, we derive explicit expressions for many low-N simple and self-intersected cases. We identify two special cases (one simple, one self-intersected) where a quantity prescribed to be invariant is actually variable.