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arXiv · 0807.4602

On the cohomological equation of magnetic flows

Nurlan S. Dairbekov·Gabriel P. Paternain
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Abstract

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 $θ$ be a smooth 1-form on $M$. We show that the cohomological equation \[\G(u)=h\circ π+θ\] has a solution $u\in C^{\infty}(SM)$ only if $h=0$ and $θ$ is closed. This result was proved in \cite{DP2} under the assumption that the flow of $\G$ is Anosov.

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Nurlan S. Dairbekov, Gabriel P. Paternain. 2008-07-29. On the cohomological equation of magnetic flows. https://arxiv.org/abs/0807.4602

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