On the cohomological equation of magnetic flows

Details On the cohomological equation of magnetic flows On the cohomological equation of magnetic flows

2008-07-29

arxiv.org/abs/0807.4602v1

Mathematics

Dynamical Systems

Scientific paper

We consider a magnetic flow without conjugate points on a closed manifold $M$ with generating vector field $\G$. Let $h\in C^{\infty}(M)$ and let $\theta$ be a smooth 1-form on $M$. We show that the cohomological equation \[\G(u)=h\circ \pi+\theta\] has a solution $u\in C^{\infty}(SM)$ only if $h=0$ and $\theta$ is closed. This result was proved in \cite{DP2} under the assumption that the flow of $\G$ is Anosov.

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