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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: g.p.paternain@dpmms.cam.ac.uk
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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

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