Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vortices over Riemann surfaces and dominated splittings   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
$(M,g)$.

27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org