An obstruction to conservation of volume in contact dynamics
| dc.creator | Polterovich, Leonid | |
| dc.date | 2000-09-26 | |
| dc.date.accessioned | 2026-07-07T04:37:42Z | |
| dc.date.available | 2026-07-07T04:37:42Z | |
| dc.description | A theorem of Moser guarantees that every diffeomorphism of a closed manifold can be isotoped to a volume preserving one. We show that this statement cannot be extended into contact category: some connected components of contactomorphism groups of certain contact manifolds contain no volume-preserving diffeomorphisms. This phenomenon can be considered from different viewpoints: geometric (isometric action of the contact mapping class group on the moduli space of contact forms), topological (action in symplectic homology) and dynamical (diffusion). We define a numerical invariant - a kind of contact Lyapunov exponent - which leads to a quantitive version of the abovementioned result. | |
| dc.description | Latex, 14 pages, preliminary version | |
| dc.identifier | https://arxiv.org/abs/math/0009227 | |
| dc.identifier | http://arxiv.org/abs/math/0009227 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59998 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Dynamical Systems | |
| dc.subject | (2000) 53Dxx (Primary) 37Jxx (Secondary) | |
| dc.title | An obstruction to conservation of volume in contact dynamics | |
| dc.type | text |