Nonlinear analysis with resurgent functions

David Sauzin (1)

1 Laboratoire Fibonacci

We provide estimates for the convolution product of an arbitrary number of ''resurgent functions'', that is holomorphic germs at the origin of $C$ that admit analytic continuation outside a closed discrete subset of $C$ which is stable under addition. Such estimates are then used to perform nonlinear operations like substitution in a convergent series, composition or functional inversion with resurgent functions, and to justify the rules of ''alien calculus''; they also yield implicitly defined resurgent functions. The same nonlinear operations can be performed in the framework of Borel-Laplace summability.

Mots clés: Resurgent functions; convolution product

Domaines: Systèmes dynamiques [math.DS]

David Sauzin. Nonlinear analysis with resurgent functions. Annales Scientifiques de l'École Normale Supérieure, 2015, 48 (3), pp.667--702. ⟨hal-00766749v4⟩