In this paper we prove that a totally integrable strictly-convex symplectic billiard table, whose boundary has everywhere strictly positive curvature, must be an ellipse. The proof, inspired by the analogous result of Bialy for Birkhoff billiards, uses the affine equivariance of the symplectic billiard map. (c) 2024 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).
Totally integrable symplectic billiards are ellipses
Baracco, Luca;Bernardi, Olga
2024
Abstract
In this paper we prove that a totally integrable strictly-convex symplectic billiard table, whose boundary has everywhere strictly positive curvature, must be an ellipse. The proof, inspired by the analogous result of Bialy for Birkhoff billiards, uses the affine equivariance of the symplectic billiard map. (c) 2024 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
1-s2.0-S0001870824003888-main (1).pdf
accesso aperto
Tipologia:
Published (Publisher's Version of Record)
Licenza:
Creative commons
Dimensione
351.23 kB
Formato
Adobe PDF
|
351.23 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
