Longitudinal KAM-cocycles and action spectra of magnetic flows
| dc.creator | Paternain, Nurlan S. Dairbekov Gabriel P. | |
| dc.date | 2005-01-11 | |
| dc.date.accessioned | 2026-07-07T05:15:59Z | |
| dc.date.available | 2026-07-07T05:15:59Z | |
| dc.description | Let $M$ be a closed oriented surface and let $Ω$ be a non-exact 2-form. Suppose that the magnetic flow $ϕ$ of the pair $(g,Ω)$ is Anosov. We show that the longitudinal KAM-cocycle of $ϕ$ is a coboundary if and only the Gaussian curvature is constant and $Ω$ is a constant multiple of the area form thus extending the results in \cite{P2}. We also show infinitesimal rigidity of the action spectrum of $ϕ$ with respect to variations of $Ω$. Both results are obtained by showing that if $G:M\to\mathbb R$ is any smooth function and $ω$ is any smooth 1-form on $M$ such that $G(x)+ω_{x}(v)$ integrates to zero along any closed orbit of $ϕ$, then $G$ must be identically zero and $ω$ must be exact. | |
| dc.identifier | https://arxiv.org/abs/math/0501172 | |
| dc.identifier | http://arxiv.org/abs/math/0501172 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73825 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Differential Geometry | |
| dc.title | Longitudinal KAM-cocycles and action spectra of magnetic flows | |
| dc.type | text |