edited by B L J Braaksma (University of Groningen, The Netherlands), G K Immink (University of Groningen, The Netherlands), M van der Put (University of Groningen, The Netherlands), & J Top (University of Groningen, The Netherlands)

This volume is the record of a workshop on differential equations and the Stokes phenomenon, held in May 2001 at the University of Groningen. It contains expanded versions of most of the lectures given at the workshop. To a large extent, both the workshop and the book may be regarded as a sequel to a conference held in Groningen in 1995 which resulted in the book The Stokes Phenomenon and Hilbert's 16th Problem (B L J Braaksma, G K Immink and M van der Put, editors), also published by World Scientific (1996).

Both books offer a snapshot concerning the state of the art in the areas of differential, difference and q-difference equations. Apart from the asymptotics of solutions, Painlevé properties and the algebraic theory, new topics addressed in the second book include arithmetic theory of linear equations, and Galois theory and Lie symmetries of nonlinear differential equations.

• Toward p-Adic Stokes Phenomena? Singularities of p-Adic Differential Equations (Y André)
• Moduli Spaces for Linear Differential Equations (M Berkenbosch)
• Factorization of Differential Operators and Application to Differential Galois Theory (M Bouffet)
• Movable Singularities of Solutions of Nonlinear Differential and Difference Equations and the Painlevé Property (O Costin & M Kruskal)
• On a Conjecture of Sophus Lie (J Draisma)
• A Tale of Three Structures: the Arithmetic of Multizetas, the Analysis of Singularities, the Lie Algebra ARI (J Ecalle)
• A Differential Intermediate Value Theorem (J van der Hoeven)
• Integrable Systems and Number Theory (P H van der Kamp et al.)
• Towards the Galois Groupoid of Nonlinear O D E (F Loray)
• Galois Theory of q-Difference Equations: The “Analytical” Approach (J Sauloy)
• “Exact WKB Integration” of the Polynomial 1D Schrödinger (or Sturm-Liouville) Problem (A Voros)
• Une Sommation Discrète Pour des Équations Aux q-Différence Linéaires et à Coefficients Analytiques: Théorie Générale et Exemples (C-G Zhang)