On the monodromy group of confluenting linear equations

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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.
24 pages, 5 figures

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Dynamical Systems, Complex Variables, 34M35, 34M40

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http://salesiana.dossiersoluciones.com/handle/123456789/67123

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0304243
 http://arxiv.org/abs/math/0304243

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arXiv