Resurgent Deformations for an Ordinary Differential Equation of Order 2

dc.creatorDelabaere, Eric
dc.creatorRasoamanana, Jean-Marc
dc.date2004-03-03
dc.date2005-02-07
dc.date.accessioned2026-07-07T05:05:55Z
dc.date.available2026-07-07T05:05:55Z
dc.descriptionWe consider in the complex field the differential equation $\displaystyle \frac{d^2}{d x^2} Φ(x) = \frac{P_m(x,\a)}{x^2}Φ(x)$, where $P_m$ is a monic polynomial function of order $m$ with coefficients $\a=(a_1, ..., a_m)$. We investigate the asymptotic, resurgent, properties of the solutions at infinity, focusing in particular on the analytic dependence on $\a$ of the Stokes-Sibuya multipliers. Taking into account the non trivial monodromy at the origin, we derive a set of functional equations for the Stokes-Sibuya multipliers. We show how these functional relations can be used to compute the Stokes multipliers for a class of polynomials $P_m$. In particular, we obtain conditions for isomonodromic deformations when $m=3$.
dc.description54 pages, 2 figures. To appear in Pac. Math. J
dc.identifierhttps://arxiv.org/abs/math/0403085
dc.identifierhttp://arxiv.org/abs/math/0403085
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70354
dc.subjectClassical Analysis and ODEs
dc.subjectComplex Variables
dc.subject34M40 34M30 24M37 81Q05
dc.titleResurgent Deformations for an Ordinary Differential Equation of Order 2
dc.typetext

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