1 results
Vortices over Riemann surfaces and dominated splittings
- Part of
-
- Journal:
- Ergodic Theory and Dynamical Systems / Volume 42 / Issue 5 / May 2022
- Published online by Cambridge University Press:
- 02 February 2021, pp. 1781-1806
- Print publication:
- May 2022
-
- Article
- Export citation
-
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 
$(M,g)$
.
