Divergent Series, Summability and Resurgence III: Resurgent Methods and the First Painlevé Equation (Lecture Notes in Mathematics)

The aim of this volume is two-fold. First, to show how
the resurgent methods introduced in volume 1 can be applied efficiently in a
non-linear setting; to this end further properties of the resurgence theory
must be developed. Second, to analyze the fundamental example of the First
Painlevé equation. The resurgent analysis of singularities is pushed all the
way up to the so-called "bridge equation", which concentrates all
information about the non-linear Stokes phenomenon at infinity of the First Painlevé
equation.



The third in a series of three, entitled Divergent Series, Summability and
Resurgence, this volume is aimed at graduate students, mathematicians and
theoretical physicists who are interested in divergent power series and related
problems, such as the Stokes phenomenon. The prerequisites are a working
knowledge of complex analysis at the first-year graduate level and of the
theory of resurgence, as presented in volume 1.