Stokes Phenomenon for Single-Level Linear Differential Systems: A Perturbative Approach

MR3364474 P. REMY P. REMY Stokes Phenomenon for Single-Level Linear Differential Systems: A Perturbative Approach Funkcialaj Ekvacioj. Serio Internacia 58 2015 177--222 http://fe.math.kobe-u.ac.jp/FE/FullPapers/58-2/58_177.pdf http://www.ams.org/mathscinet-getitem?mr=MR3364474 Given a meromorphic linear differential system with an arbitrary single level $r \geq1$, we build a regular holomorphic perturbation which preserves the single level and we show that the Stokes-Ramis matrices of the initial system are limits of convenient products of the perturbed ones. As an application, we provide an alternative method for the effective calculation of the Stokes multipliers of the initial system illustrated on two examples. No assumption of genericity is made on the initial system. Linear differential system, Regular perturbation, Holomorphic perturbation, Stokes phenomenon, Summability, Stokes multipliers. 34M03, 34M30, 34M40. 58-177 2015 Stokes Phenomenon for Single-Level Linear Differential Systems: A Perturbative Approach P. REMY P. REMY 1 Balser, W.; Jurkat, W. B.; Lutz, D. A. A general theory of invariants for meromorphic differential equations; Part I, formal invariants Funkcial. Ekvac. 22 1979 197-221 MR0556577 0556577 2 Écalle, J. Les fonctions résurgentes, tome III: l'équation du pont et la classification analytique des objets locaux Publications Mathématiques d'Orsay, 85-5, Université de Paris-Sud, Département de Mathématiques, Orsay 1985 MR0852210

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