Resurgent functions and nonlinear systems of differential and difference equations

TL;DR

This paper develops an iteration method for resurgent functions, demonstrating how it can establish the resurgence of formal solutions to nonlinear differential and difference equations through convolution estimates.

Contribution

It introduces a new iteration technique on resurgent functions and applies it to prove resurgence of solutions in nonlinear differential and difference equations.

Findings

Established an iteration method for resurgent functions

Proved resurgence of formal solutions to nonlinear equations

Developed convolution estimates for resurgent functions

Abstract

The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the method in arXiv:1610.05453. Using the estimates, we show the resurgence of formal series solutions of nonlinear differential and difference equations.