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.
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Springer International Publishing
Illustrationen
14
21 s/w Abbildungen, 14 farbige Abbildungen
XXII, 230 p. 35 illus., 14 illus. in color.
Dateigröße
ISBN-13
978-3-319-29000-3 (9783319290003)
DOI
10.1007/978-3-319-29000-3
Schweitzer Klassifikation
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.
