These two bound volumes present the proceedings of the conference, Complex Analysis, Dynamical Systems, Summability of Divergent Series and Galois Theories, held in Toulouse on the occasion of J.-P. Ramis' sixtieth birthday.

The first volume opens with two articles composed of recollections and three articles on J.-P. Ramis' works on complex analysis and ODE theory, both linear and non-linear. This introduction is followed by papers concerned with Galois theories, arithmetic or integrability: analogies between differential and arithmetical theories, \(q\)-difference equations, classical or \(p\)-adic, the Riemann-Hilbert problem and renormalization, \(b\)-functions, descent problems, Krichever modules, the set of integrability, Drach theory, and the VI\({}^{{th}}\) Painlevé equation.

The second volume contains papers dealing with analytical or geometrical aspects: Lyapunov stability, asymptotic and dynamical analysis for pencils of trajectories, monodromy in moduli spaces, WKB analysis and Stokes geometry, first and second Painlevé equations, normal forms for saddle-node type singularities, and invariant tori for PDEs.

The volumes are suitable for graduate students and researchers interested in differential equations, number theory, geometry, and topology.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and researchers interested in differential equations, number theory, geometry, and topology.

Table of Contents

• B. Malgrange -- Les premiers travaux de Jean-Pierre Ramis
• G. Ruget -- Témoignage
• D. Bertrand -- Travaux de J.-P. Ramis sur les équations différentielles linéaires
• D. Cerveau -- Travaux de J.-P. Ramis sur les équations différentielles non linéaires
• M. Loday-Richaud -- Souvenirs strasbourgeois
• Y. André -- Galois representations, differential equations, and \(q\)-difference equations: sketch of a \(p\)-adic unification
• Y. André and L. Di Vizio -- \(q\)-difference equations and \(p\)-adic local monodromy
• A. Connes -- Renormalisation et ambiguité galoisienne
• Y. Laurent -- \(b\)-functions and integrable solutions of holonomic \(\mathcal D\)-module
• A. L. Neto -- Curvature of pencils of foliations
• M. van der Put -- Skew differential fields, differential and difference equations
• M. van der Put and M. Reversat -- Krichever modules for difference and differential equations
• J. Sauloy -- Algebraic construction of the Stokes sheaf for irregular linear \(q\)-difference equations
• H. Umemura -- Monodromy preserving deformation and differential Galois group I

• F. Cano, R. Moussu, and F. Sanz -- Pinceaux de courbes intégrales d'un champ de vecteurs analytique
• B. Dubrovin -- On analytic families of invariant tori for PDEs
• N. Joshi, K. Kahwara, and M. Mazzocco -- Generating function associated with the determinant formula for the solutions of the Painlevé II equation
• V. Kaloshin, J. N. Mather, and E. Valdinoci -- Instability of resonant totally elliptic points of symplectic maps in dimension \(4\)
• T. Kawai, T. Koike, Y. Nishikawa, and Y. Takei -- On the Stokes geometry of higher order Painlevé equations
• F. Loray -- Versal deformation of the analytic saddle-node
• C. Simpson -- Asymptotics for general connections at infinity