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
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 $(M,g)$.
