We study more invariants in the elliptic billiard, including those manifested by self-intersected orbits and inversive polygons . We also derive expressions for some entries in "Eighty New Invariants of N-Periodics in the Elliptic Billiard" (2020), arXiv:2004.12497  .
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 .
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more invariants
self-intersected N-periodics
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including those manifested by
describing new facts about their geometry (e.g.,
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orbits and inversive polygons
4-periodics have vertices concyclic with the foci)
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derive expressions for some entries
check if some invariants listed
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, 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