Introduction to 1-summability and the resurgence theory

David Sauzin (1)

1 Laboratoire Fibonacci

This text is about the mathematical use of certain divergent power series. The first part is an introduction to 1-summability. The second part is an introduction to Ecalle's resurgence theory. A few elementary or classical examples are given a thorough treatment (the Euler series, the Stirling series, a less known example by Poincaré). Special attention is devoted to non-linear operations and original demonstrations are included. The resurgent approach to the classification of tangent-to-identity germs of holomorphic diffeomorphisms in the simplest case is also included.

Mots clés: Summability; Borel transform; Laplace transform; resurgent functions; convolution product

Domaines: Systèmes dynamiques [math.DS]; Analyse classique [math.CA]

David Sauzin. Introduction to 1-summability and the resurgence theory. 2013. ⟨hal-00860032v1⟩