Poncelet pairs and the Twist Map associated to the Poncelet Billiard
| dc.creator | Lopes, Artur O. | |
| dc.creator | Sebastiani, M. | |
| dc.date | 2007-05-28 | |
| dc.date | 2008-03-17 | |
| dc.date.accessioned | 2026-07-07T09:26:44Z | |
| dc.date.available | 2026-07-07T09:26:44Z | |
| dc.description | We show that for a fixed curve $K$ and for a family of variables curves $L$, the number of $n$-Poncelet pairs is $\frac{e (n)}{2}$, where $e(n)$ is the number of natural numbers $m$ smaller than $n$ and which satisfies mcd $ (m,n)=1$. The curvee $K$ do not have to be part of the family. In order to show this result we consider an associated billiard transformation and a twist map which preserves area. We use Aubry-Mather theory and the rotation number of invariant curves to obtain our main result. In the last section we estimate the derivative of the rotation number of a general twist map using some properties of the continued fraction expansion . | |
| dc.identifier | https://arxiv.org/abs/0705.4057 | |
| dc.identifier | http://arxiv.org/abs/0705.4057 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156857 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Mathematical Physics | |
| dc.subject | 37D50; 37E40 | |
| dc.title | Poncelet pairs and the Twist Map associated to the Poncelet Billiard | |
| dc.type | text |