Eighty New Invariants of N-Periodics in the Elliptic Billiard

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.

17 pages, 9 figures, 12 tables, 18 video links

References in corpus (2)

• Can the Elliptic Billiard Still Surprise Us?
• Eighty New Invariants of N-Periodics in the Elliptic Billiard

Cited by in corpus (7)

• Eighty New Invariants of N-Periodics in the Elliptic Billiard
• Loci of 3-periodics in an Elliptic Billiard: why so many ellipses?
• Mather $\beta$-function for ellipses and rigidity
• New Invariants of Poncelet-Jacobi Bicentric Polygons
• The Talented Mr. Inversive Triangle in the Elliptic Billiard
• Parable of the Parabola
• Poncelet Plectra: Harmonious Curves in Cosine Space