The Stokes phenomenon in exact asymptotics
type: Item
instance of: scholarly article
title: The Stokes phenomenon in exact asymptotics
zbMATH Open document ID: 0952.34074
author: V. Pereyra
published in: Pacific Journal of Mathematics
publication date: 2000-08-23T00:00:00Z
review text: The paper begins with a new and elementary constructive proof for the multisummability properties of formal solutions to linear ordinary differential equations at irregular singular points. This then serves as a model to illustrate the geometric approach to multisummation. Several basic properties of multisums and the associated sheaves are derived. The paper then moves on to study the Cauchy-Heine transforms in relation to multisummation and the Stokes phenomenon. The authors then show how to construct multisums with a prescribed Stokes phenomenon using the Malgrange-Sibuya isomorphism. Starting with the Stokes automorphisms the authors introduce the alien derivations of J. Ecalle and derive the Ecalle's bridge equation for the general integral linear ordinary differential equations. All the main ideas are clearly illustrated with some very lucid examples.
Mathematics Subject Classification ID: 34M40
Mathematics Subject Classification ID: 34M30
Mathematics Subject Classification ID: 30D10
zbMATH DE Number: 1344276
zbMATH Keywords: Stokes phenomenon
zbMATH Keywords: exact asymptotics
zbMATH Keywords: irregular singular points
zbMATH Keywords: multisummation
zbMATH Keywords: Cauchy-Heine transforms
zbMATH Keywords: Malgrange-Sibuya isomorphism
reviewed by: John Schmeelk
MaRDI profile type: Publication
full work available at URL: pjm.1999.187.13
OpenAlex ID: W2020769478
DOI: 10.2140/PJM.1999.187.13
description: scientific article; zbMATH DE number 1344276