03109cam a2200445 i 4500991003531689707536m o d cr cnu|||unuuu180807s2016 sz a ob 001 0 eng d9783319290003331929000210.1007/978-3-319-29000-3b14348172-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng515.24323AMS 40-02LC QA295Delabaere, Éric730101Divergent series, summability and resurgence III[e-book] :Resurgent methods and the first Painlevé equation /Eric DelabaereResurgent methods and the first Painlevé equationCham, Switzerland :Springer,20161 online resource (xxii, 230 pages) :illustrations (some color)texttxtrdacontentcomputercrdamediaonline resourcecrrdacarrierLecture notes in mathematics,0075-8434 ;2155Includes bibliographical references and indexAvant-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 ; IndexThe 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 1Divergent seriesSummability theoryPainlevé equationsSpringerLink (Online service)Springer eBookshttps://link.springer.com/book/10.1007/978-3-319-29000-3An electronic book accessible through the World Wide Web.b1434817203-03-2207-08-18991003531689707536Divergent series, summability and resurgence III1748966UNISALENTOle01307-08-18m@ -engsz 00