论文标题

Riemann表面上的涡流和主导的分裂

Vortices over Riemann surfaces and dominated splittings

论文作者

Mettler, Thomas, Paternain, Gabriel P.

论文摘要

我们将Flow $ ϕ $与封闭式的Riemannian 2-Manifold $(m,g)$的负欧拉特征的涡旋方程的解决方案相关联,并调查其属性。我们表明,$ ϕ $总是承认主导的分裂,并确定$ ϕ $为Anosov的特殊情况。特别是,从分数程度的全体形态差异开始,我们在单位切线束的合适根部(m,g)$的单位切线上产生了新颖的例子。

We associate a flow $ϕ$ 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 $ϕ$ always admits a dominated splitting and identify special cases in which $ϕ$ 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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