TY  - BOOK
AU  - Delabaere,Eric
TI  - Divergent series, summability and resurgence III: resurgent methods and the first Painleve equation 
T2  - Lecture notes in mathematics
SN  - 9783319289991
U1  - 515.243 23
PY  - 2016///
CY  - Switzerland : 
PB  - Springer
KW  - Divergent series.
KW  - Summability theory.
N1  - Includes bibliographical references and index; 1. Some Elements about Ordinary Differential Equations Delabaere --
2. The First Painleve Equation Delabaere --
3. Tritruncated Solutions For The First Painleve Equation --
4. A Step Beyond Borel-Laplace Summability --
5. Transseries And Formal Integral For The First Painleve Equation --
6. Truncated Solutions For The First Painleve Equation --
7. Supplements To Resurgence Theory --
8. Resurgent Structure For The First Painleve Equation
N2  - 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
ER  -