Exponential asymptotics, transseries, and generalized Borel summation for analytic rank one systems of ODE's
| dc.creator | Costin, O. | |
| dc.date | 2006-08-16 | |
| dc.date.accessioned | 2026-07-07T07:21:51Z | |
| dc.date.available | 2026-07-07T07:21:51Z | |
| dc.description | For analytic nonlinear systems of ordinary differential equations, under some non-degeneracy and integrability conditions we prove that the formal exponential series solutions (trans-series) at an irregular singularity of rank one are Borel summable (in a sense similar to that of Ecalle). The functions obtained by re-summation of the trans-series are precisely the solutions of the differential equation that decay in a specified sector in the complex plane. We find the dependence of the correspondence between the solutions of the differential equation and trans-series as the ray in the complex plane changes (local Stokes phenomenon). We study, in addition, the general solution in $\lloc$ of the convolution equations corresponding, by inverse Laplace transform, to the given system of ODE's, and its analytic properties. Simple analytic identities lead to ``resurgence'' relations and to an averaging formula having, in addition to the properties of the medianization of Ecalle, the property of preserving exponential growth at infinity. | |
| dc.identifier | https://arxiv.org/abs/math/0608414 | |
| dc.identifier | http://arxiv.org/abs/math/0608414 | |
| dc.identifier | IMRN 8, (1995) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115448 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 34E10,34M30,34M37,34M40 | |
| dc.title | Exponential asymptotics, transseries, and generalized Borel summation for analytic rank one systems of ODE's | |
| dc.type | text |