Thesis-2018-Horrobin.pdf (4.35 MB)
Stokes' Phenomenon arising from the confluence of two simple poles
thesisposted on 2018-02-02, 10:08 authored by Calum Horrobin
We study certain confluences of equations with two Fuchsian singularities which produce an irregular singularity of Poincaré rank one. We demonstrate a method to understand how to pass from solutions with power-like behavior which are analytic in neighbourhoods to solutions with exponential behavior which are analytic in sectors and have divergent asymptotic behavior. We explicitly calculate the Stokes' matrices of the confluent system in terms of the monodromy data, specifically the connection matrices, of the original system around the merging singularities. The confluence of Gauss' hypergeometric equation gives an excellent opportunity to show our approach with a concrete example. We explicitly show how the Stokes' data arise in the confluences of the isomonodromic deformation problems for the Painlevé equations PVI to PV and PV to PIII(D6).
- Mathematical Sciences
Publisher© Horrobin, Calum
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
NotesA Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.