Divergent Series, Summability and Resurgence III : Resurgent Methods and the First Painlevé Equation / by Eric Delabaere

By:

Delabaere, Eric [aut]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink Bücher | Lecture notes in mathematics ; 2155Publisher: Cham : Springer, 2016Description: Online-Ressource (XXII, 230 p. 35 illus., 14 illus. in color, online resource)ISBN:

9783319290003

Subject(s):

Additional physical formats: 9783319289991 | Druckausg.: Divergent series, summability and resurgence ; 3: Resurgent methods and the first Painlevé equation. [Cham] : Springer International Publishing Switzerland, 2016. xxii, 230 SeitenMSC: MSC: *34-02 | 34M30 | 34M40 | 34M55 | 40-02RVK: RVK: SI 850LOC classification:

QA292 QA295
QA292
QA295

DOI: DOI: 10.1007/978-3-319-29000-3Online resources:

Summary: 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. .PPN: PPN: 1657705145Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-LNM | ZDB-2-SMA

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