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- W2952862729 abstract "Let $M$ be a closed oriented surface endowed with a Riemannian metric $g$ and let $Omega$ be a 2-form. We show that the magnetic flow of the pair $(g,Omega)$ has zero asymptotic Maslov index and zero Liouville action if and only $g$ has constant Gaussian curvature, $Omega$ is a constant multiple of the area form of $g$ and the magnetic flow is a horocycle flow. This characterization of horocycle flows implies that if the magnetic flow of a pair $(g,Omega)$ is $C^1$-conjugate to the horocycle flow of a hyperbolic metric $bar{g}$ then there exists a constant $a>0$, such that $ag$ and $bar{g}$ are isometric and $a^{-1}Omega$ is, up to a sign, the area form of $g$. The characterization also implies that if a magnetic flow is Ma~n'e critical and uniquely ergodic it must be the horocycle flow. As a by-product we also obtain results on existence of closed magnetic geodesics for almost all energy levels in the case weakly exact magnetic fields on arbitrary manifolds." @default.
- W2952862729 created "2019-06-27" @default.
- W2952862729 creator A5025386563 @default.
- W2952862729 date "2004-09-27" @default.
- W2952862729 modified "2023-09-27" @default.
- W2952862729 title "Magnetic Rigidity of Horocycle flows" @default.
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- W2952862729 hasPublicationYear "2004" @default.
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