Delabaere, Eric; Rasoamanana, Jean-Marc Resurgent deformations for an ordinary differential equation of order 2. (English) Zbl 1116.34068 Pac. J. Math. 223, No. 1, 35-93 (2006). The paper is the first of three papers to come. The authors consider the second order differential equation \[ (d^2/dx^2)\Phi (x)=(P_m(x)/x^2)\Phi (x) \]in the complex domain, where the monic polynomial \(P_m\) is of degree \(m\). They investigate the asymptotic and resurgent properties of its solutions at infinity, in particular – the dependence of the Stokes-Sibuya multipliers (SSM) on the coefficients of \(P_m\). They derive a set of functional equations for the SSM (taking into account the nontrivial monodromy at the origin) and show how these equations can be used to compute the SSM for a class of polynomials \(P_m\). In particular, they obtain conditions for isomonodromic deformations when \(m=3\). Reviewer: Vladimir P. Kostov (Nice) Cited in 4 Documents MSC: 34M37 Resurgence phenomena (MSC2000) 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) 34M40 Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain Keywords:resurgence theory; Stokes phenomena; connection problem; alien derivations; Borel-resummable series; Stokes-Sibuya connection matrix; isomonodromic deformation PDFBibTeX XMLCite \textit{E. Delabaere} and \textit{J.-M. Rasoamanana}, Pac. J. Math. 223, No. 1, 35--93 (2006; Zbl 1116.34068) Full Text: DOI arXiv