Volume preserving bi-Lipschitz homeomorphisms on the Heisenberg group
| dc.creator | Buliga, Marius | |
| dc.date | 2002-05-04 | |
| dc.date | 2002-05-24 | |
| dc.date.accessioned | 2026-07-07T04:48:16Z | |
| dc.date.available | 2026-07-07T04:48:16Z | |
| dc.description | Elementary sub-Riemannian geometry on the Heisenberg group H(n) provides a compact picture of symplectic geometry. Any Hamiltonian diffeomorphism on $R^{2n}$ lifts to a volume preserving bi-Lipschitz homeomorphisms of H(n), with the use of its generating function. Any curve of a flow of such homeomorphisms deviates from horizontality by the Hamiltonian of the flow. From the metric point of view this means that any such curve has Hausdorff dimension 2 and the $\mathcal{H}^{2}$ (area) density equal to the Hamiltonian. The non-degeneracy of the Hofer distance is a direct consequence of this fact. | |
| dc.identifier | https://arxiv.org/abs/math/0205039 | |
| dc.identifier | http://arxiv.org/abs/math/0205039 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63978 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Metric Geometry | |
| dc.subject | 53D35; 53C17 | |
| dc.title | Volume preserving bi-Lipschitz homeomorphisms on the Heisenberg group | |
| dc.type | text |