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arXiv · 2004.12497

Eighty New Invariants of N-Periodics in the Elliptic Billiard

Dan Reznik·Ronaldo Garcia·Jair Koiller
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Abstract

We introduce several-dozen experimentally-found invariants of Poncelet N-periodics in the confocal ellipse pair (Elliptic Billiard). Recall this family is fully defined by two integrals of motion (linear and angular momentum), so any "new" invariants are dependent upon them. Nevertheless, proving them may require sophisticated methods. We reference some two-dozen proofs already contributed. We hope this article will motivate contributions for those still lacking proof.

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Dan Reznik, Ronaldo Garcia, Jair Koiller. 2020-04-26. Eighty New Invariants of N-Periodics in the Elliptic Billiard. https://doi.org/10.1007/s40598-021-00174-y

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