On the monodromy group of confluent linear equations

We consider a linear analytic ordinary differential equation with complex time having a nonresonant irregular singular point. We study it as a limit of a generic family of equations with confluent Fuchsian singularities.
In 1984, V. I. Arnold asked the following question: Is it true that some operators from the monodromy group of the perturbed (Fuchsian) equation tend to Stokes operators of the nonperturbed irregular equation? Another version of this question was also proposed independently by J.-P. Ramis in 1988.
We consider only the case of Poincaré rank 1. We show (in dimension two) that, generically, no monodromy operator tends to a Stokes operator; on the other hand, in any dimension, the commutators of appropriate noninteger powers of the monodromy operators around singular points tend to Stokes operators.