Divergent Series, Summability and Resurgence III

The aim of this volume is two-fold. First, to show howthe resurgent methods introduced in volume 1 can be applied efficiently in anon-linear setting; to this end further properties of the resurgence theorymust be developed. Second, to analyze the fundamental example of the FirstPainlevé equation. The resurgent analysis of singularities is pushed all theway up to the so-called “bridge equation”, which concentrates allinformation about the non-linear Stokes phenomenon at infinity of the