Article contents
Vortices over Riemann surfaces and dominated splittings
Published online by Cambridge University Press: 02 February 2021
Abstract
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
$(M,g)$
.
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- © The Author(s), 2021. Published by Cambridge University Press
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