A note on the computation of Puiseux series solutions of the Riccatti equation associated with a homogeneous linear ordinary differential equation

We present in this paper a detailed note on the computation of Puiseux series solutions of the Riccatti equation associated with a homogeneous linear ordinary differential equation. This paper is a continuation of [1] which was on the complexity of solving arbitrary ordinary polynomial differential equations in terms of Puiseux series

Resurgence and holonomy of the ϕ2k\phi^{2k} model in zero dimension

We describe the resurgence properties of some partition functions corresponding to field theories in dimension 0. We show that these functions satisfy linear differential equations with polynomial coefficients and then use elementary stability results or holonomic functions to prove resurgence properties, enhancing previously known results on growth estimates for the formal series involved, which had been obtained through a delicate combinatorics.Comment: 38 pages, 7 figure

Asymptotic Differential Algebra and Model Theory of Transseries

We develop here the algebra of the differential field of transseries and of related valued differential fields. This book contains in particular our recently obtained decisive positive results on the model theory of these structures.Comment: 729 pp; version 6 correcting various smaller mistakes; for a list of errata to the printed version see http://www.math.ucla.edu/~matthias/pdf/mt-errata.pd