Quasiperiodic Motion for the Pentagram Map
| dc.creator | Ovsienko, Valentin | |
| dc.creator | Schwartz, Richard | |
| dc.creator | Tabachnikov, Serge | |
| dc.date | 2009-01-12 | |
| dc.date.accessioned | 2026-07-07T12:28:26Z | |
| dc.date.available | 2026-07-07T12:28:26Z | |
| dc.description | The pentagram map is a projectively natural iteration defined on polygons, and also on a generalized notion of a polygon which we call {\it twisted polygons}. In this note we describe our recent work on the pentagram map, in which we find a Poisson structure on the space of twisted polygons and show that the pentagram map relative to this Poisson structure is completely integrable in the sense of Arnold-Liouville. For certain families of twisted polygons, such as those we call {\it universally convex}, we translate the integrability into a statement about the quasi-periodic notion of the pentagram-map orbits. We also explain how the continuous limit of the Pentagram map is the classical Boissinesq equation, a completely integrable PDE. | |
| dc.description | This note is a short announcement of arXiv:0810.5605 | |
| dc.identifier | https://arxiv.org/abs/0901.1585 | |
| dc.identifier | http://arxiv.org/abs/0901.1585 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215538 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | 37J35 (Primary), 51A99 (Secondary) | |
| dc.title | Quasiperiodic Motion for the Pentagram Map | |
| dc.type | text |