The Stokes phenomenon in exact asymptotics
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.
scientific article; zbMATH DE number 1344276