Magnetic Rigidity of Horocycle flows
| dc.creator | Paternain, Gabriel P. | |
| dc.date | 2004-09-27 | |
| dc.date.accessioned | 2026-07-07T05:12:38Z | |
| dc.date.available | 2026-07-07T05:12:38Z | |
| dc.description | Let $M$ be a closed oriented surface endowed with a Riemannian metric $g$ and let $Ω$ be a 2-form. We show that the magnetic flow of the pair $(g,Ω)$ has zero asymptotic Maslov index and zero Liouville action if and only $g$ has constant Gaussian curvature, $Ω$ is a constant multiple of the area form of $g$ and the magnetic flow is a horocycle flow. This characterization of horocycle flows implies that if the magnetic flow of a pair $(g,Ω)$ is $C^1$-conjugate to the horocycle flow of a hyperbolic metric $\bar{g}$ then there exists a constant $a>0$, such that $ag$ and $\bar{g}$ are isometric and $a^{-1}Ω$ is, up to a sign, the area form of $g$. The characterization also implies that if a magnetic flow is Mañé critical and uniquely ergodic it must be the horocycle flow. As a by-product we also obtain results on existence of closed magnetic geodesics for almost all energy levels in the case weakly exact magnetic fields on arbitrary manifolds. | |
| dc.identifier | https://arxiv.org/abs/math/0409528 | |
| dc.identifier | http://arxiv.org/abs/math/0409528 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72648 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Differential Geometry | |
| dc.title | Magnetic Rigidity of Horocycle flows | |
| dc.type | text |