Loughborough University
Leicestershire, UK
LE11 3TU
+44 (0)1509 263171
Loughborough University

Loughborough University Institutional Repository

Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/28357

Title: Stokes' Phenomenon arising from the confluence of two simple poles
Authors: Horrobin, Calum
Keywords: Painlevé equations
Hypergeometric differential equations
Confluence
Monodromy
Isomonodromic deformations
Asymptotic expansions
Analytic functions.
Issue Date: 2018
Publisher: © Horrobin, Calum
Abstract: 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).
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.
Sponsor: EPSRC.
URI: https://dspace.lboro.ac.uk/2134/28357
Appears in Collections:PhD Theses (Maths)

Files associated with this item:

File Description SizeFormat
Thesis-2018-Horrobin.pdf4.46 MBAdobe PDFView/Open
Form-2018-Horrobin.pdf350.79 kBAdobe PDFView/Open

 

SFX Query

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.