C^0-rigidity of Poisson brackets
| dc.creator | Entov, Michael | |
| dc.creator | Polterovich, Leonid | |
| dc.date | 2007-12-18 | |
| dc.date.accessioned | 2026-07-07T08:49:52Z | |
| dc.date.available | 2026-07-07T08:49:52Z | |
| dc.description | Consider a functional associating to a pair of compactly supported smooth functions on a symplectic manifold the maximum of their Poisson bracket. We show that this functional is lower semi-continuous with respect to the product uniform (C^0) norm on the space of pairs of such functions. This extends previous results of Cardin-Viterbo and Zapolsky. The proof involves theory of geodesics of the Hofer metric on the group of Hamiltonian diffeomorphisms. We also discuss a failure of a similar semi-continuity phenomenon for multiple Poisson brackets of three or more functions. | |
| dc.description | Latex, 11 pages | |
| dc.identifier | https://arxiv.org/abs/0712.2913 | |
| dc.identifier | http://arxiv.org/abs/0712.2913 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144458 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 53D35, 53D05 | |
| dc.title | C^0-rigidity of Poisson brackets | |
| dc.type | text |