Divergent Series, Summability and Resurgence III [electronic resource] : Resurgent Methods and the First Painlevé Equation / by Eric Delabaere.

By: Delabaere, Eric [author.]Contributor(s): SpringerLink (Online service)Material type: TextTextSeries: Lecture Notes in Mathematics ; 2155Publisher: Cham : Springer International Publishing : Imprint: Springer, 2016Edition: 1st ed. 2016Description: XXII, 230 p. 35 illus., 14 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319290003Subject(s): Sequences (Mathematics) | Differential equations | Functions of complex variables | Special functions | Sequences, Series, Summability | Ordinary Differential Equations | Functions of a Complex Variable | Special FunctionsAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 515.24 LOC classification: QA292QA295Online resources: Click here to access online
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.
In: Springer Nature eBookSummary: 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. .
Item type: E-BOOKS
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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.

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. .

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