We associate a flow $\phi $ with 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 $(M,g)$ .

中文翻译：

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黎曼曲面上的涡旋和主分裂

我们将流 $\phi $ 与具有负欧拉特征的封闭定向黎曼 2 流形 $(M,g)$ 上的涡旋方程的解相关联，并研究其性质。我们证明 $\phi $ 总是承认一个支配分裂，并确定 $\phi $ 是 Anosov 的特殊情况。特别是，从分数阶的全纯微分开始，我们在 $(M,g)$ 的单位切丛的合适根上产生了 Anosov 流的新示例。