Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-29T18:19:35.379Z Has data issue: false hasContentIssue false
  • English
  • Français

The longitudinal KAM-cocycle of a magnetic flow

Published online by Cambridge University Press:  05 September 2005

GABRIEL P. PATERNAIN
GABRIEL P. PATERNAIN
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge CB 3 0WB. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Let $M$ be a closed oriented surface of negative Gaussian curvature and let $\Omega$ be a non-exact 2-form. Let $\lambda$ be a small positive real number. We show that the longitudinal KAM-cocycle of the magnetic flow given by $\la\,\Omega$ is a coboundary if and only if the Gaussian curvature is constant and $\Omega$ is a constant multiple of the area form.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 139 , Issue 2 , September 2005 , pp. 307 - 316
Copyright
2005 Cambridge Philosophical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)