2003/04/17 by Alexey Glutsyuk, Glutsyuk, Alexey
Computer Science · Mathematics · #34M35 #34M40 #Analytic and geometric function theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Matrix Theory and Algorithms #math.CV #math.DS #msc:34M35 #msc:34M40
paper · pdf · doi:10.48550/arxiv.math/0304243
24 pages, 5 figures
arxiv created 2003/04/17 · openalex publication_date 2003/04/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 confluenting 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 independently proposed by J.-P.Ramis in 1988. We consider the case of Poincaré rank 1 only. We show (in dimension two) that generically no monodromy operator tends to a Stokes operator; on the other hand, in any dimension commutators of appropriate noninteger powers of the monodromy operators around singular points tend to Stokes operators.