Chaotic Geodesics in Carnot Groups
| dc.creator | Montgomery, R. | |
| dc.creator | Shapiro, M. | |
| dc.creator | Stolin, A. | |
| dc.date | 1997-04-25 | |
| dc.date.accessioned | 2026-07-07T09:13:04Z | |
| dc.date.available | 2026-07-07T09:13:04Z | |
| dc.description | The group of real 4 by 4 upper triangular matrices with 1s on the diagonal has a left-invariant subRiemannian (or Carnot-Caratheodory) structure whose underlying distribution corresponds to the superdiagonal. We prove that the associated subRiemannian geodesic flow is not completely integrable. This provides the first example of a Carnot group (graded nilpotent Lie group with an invariant subRiemannian structure supported on the generating subspace) with a non-integrable geodesic flow. We apply this result to prove that the centralizer for the corresponding quadratic ``quantum'' Hamiltonian in the universal enveloping algebra for this group is ``as small as possible''. | |
| dc.description | LaTeX, 10 pages | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9704013 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9704013 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152237 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53Cxx, 53C22, 58F07, 58A30 | |
| dc.title | Chaotic Geodesics in Carnot Groups | |
| dc.type | text |