Resurgent Deformations for an Ordinary Differential Equation of Order 2
| dc.creator | Delabaere, Eric | |
| dc.creator | Rasoamanana, Jean-Marc | |
| dc.date | 2004-03-03 | |
| dc.date | 2005-02-07 | |
| dc.date.accessioned | 2026-07-07T05:05:55Z | |
| dc.date.available | 2026-07-07T05:05:55Z | |
| dc.description | We 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.description | 54 pages, 2 figures. To appear in Pac. Math. J | |
| dc.identifier | https://arxiv.org/abs/math/0403085 | |
| dc.identifier | http://arxiv.org/abs/math/0403085 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70354 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Complex Variables | |
| dc.subject | 34M40 34M30 24M37 81Q05 | |
| dc.title | Resurgent Deformations for an Ordinary Differential Equation of Order 2 | |
| dc.type | text |