  In 2004, Enriquez-Etingof-Marshall suggested a new approach to the
Ginzburg-Weinstein linearization theorem for a quasitriangular Lie bialgebra
$(\g,r)$. This approach is based on solving a system of PDEs for a gauge
transformation between the classical r-matrix $r$ and the Alekseev-Meinrenken
dynamical r-matrix. They proved that the semiclassical limit of an admissible
Drinfeld twist gives rise to a solution of the PDEs.
  In this paper, we explain that preferred gauge transformations can be
constructed as connection maps for a certain irregular Riemann-Hilbert problem
(provided $r$ is the standard classical r-matrix). Along the way, we give a
symplectic geometric interpretation of their PDEs, as a symplectic neighborhood
version of the Ginzburg-Weinstein linearization theorem. Our construction is
based on earlier works by Boalch. We then prove that for semisimple Lie algebra
$\g$, any solution of the PDEs for the gauge transformation is the
semiclassical limit of an admissible Drinfeld twist. As byproducts, we find a
surprising relation between the connection maps and Drinfeld twists as well as
a new description of the Lu-Weinstein symplectic double.
