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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 First Painlevéequation.
The third in a series of three, entitled Divergent Series, Summability andResurgence, this volume is aimed at graduate students, mathematicians andtheoretical physicists who are interested in divergent power series and relatedproblems, such as the Stokes phenomenon. The prerequisites are a workingknowledge of complex analysis at the first-year graduate level and of thetheory of resurgence, as presented in volume 1.
List of contents
Avant-Propos.- Preface to the three volumes.- Preface to this volume.- Some elements about ordinary differential equations.- The first Painlevé equation.- Tritruncated solutions for the first Painlevé equation.- A step beyond Borel-Laplace summability.- Transseries and formal integral for the first Painlevé equation.- Truncated solutions for the first Painlevé equation.- Supplements to resurgence theory.- Resurgent structure for the first Painlevé equation.- Index.
Summary
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.
