The longitudinal KAM-cocycle of a magnetic flow

Details The longitudinal KAM-cocycle of a magnetic flow The longitudinal KAM-cocycle of a magnetic flow

2004-05-31

arxiv.org/abs/math/0405598v1

Mathematics

Dynamical Systems

Scientific paper

10.1017/S0305004105008613

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.

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