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arXiv · 2002.03684

Vortices over Riemann surfaces and dominated splittings

Thomas Mettler·Gabriel P. Paternain
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Abstract

We associate a flow $\phi$ to a solution of the vortex equations on a closed oriented Riemannian 2-manifold $(M,g)$ of negative Euler characteristic and investigate its properties. We show that $\phi$ always admits a dominated splitting and identify special cases in which $\phi$ is Anosov. In particular, starting from holomorphic differentials of fractional degree, we produce novel examples of Anosov flows on suitable roots of the unit tangent bundle of $(M,g)$.

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Thomas Mettler, Gabriel P. Paternain. 2020-02-10. Vortices over Riemann surfaces and dominated splittings. https://doi.org/10.1017/etds.2020.142

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