Confluence of singularities of non-linear differential equations via Borel--Laplace transformations
Classical Analysis and ODEs
2015-11-04 v3 Complex Variables
Dynamical Systems
Abstract
Borel summable divergent series usually appear when studying solutions of analytic ODE near a multiple singular point. Their sum, uniquely defined in certain sectors of the complex plane, is obtained via the Borel--Laplace transformation. This article shows how to generalize the Borel--Laplace transformation in order to investigate bounded solutions of parameter dependent non-linear differential systems with two simple (regular) singular points unfolding a double (irregular) singularity. We construct parametric solutions on domains attached to both singularities, that converge locally uniformly to the sectoral Borel sums. Our approach provides a unified treatment for all values of the complex parameter.
Keywords
Cite
@article{arxiv.1307.8383,
title = {Confluence of singularities of non-linear differential equations via Borel--Laplace transformations},
author = {Martin Klimes},
journal= {arXiv preprint arXiv:1307.8383},
year = {2015}
}
Comments
42 pages