Eighty New Invariants of N-Periodics in the Elliptic Billiard
This work provides new invariants for researchers in dynamical systems and geometry, but it is incremental as they are derived from known integrals.
The authors introduced dozens of experimentally discovered invariants for Poncelet N-periodics in an elliptic billiard system, which are dependent on existing integrals of motion, and noted that some proofs are still needed.
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.