Use this URL to cite or link to this record in EThOS:
Title: Stokes' Phenomenon arising from the confluence of two simple poles
Author: Horrobin, Calum
ISNI:       0000 0004 7232 8486
Awarding Body: Loughborough University
Current Institution: Loughborough University
Date of Award: 2018
Availability of Full Text:
Access from EThOS:
Access from Institution:
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).
Supervisor: Not available Sponsor: EPSRC
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Painleve´ equations ; Hypergeometric differential equations ; Confluence ; Monodromy ; Isomonodromic deformations ; Asymptotic expansions ; Analytic functions.