LEADER 03915nam 22006375 450 001 996466770303316 005 20200705022942.0 010 $a3-319-29000-2 024 7 $a10.1007/978-3-319-29000-3 035 $a(CKB)3710000000734916 035 $a(DE-He213)978-3-319-29000-3 035 $a(MiAaPQ)EBC5586319 035 $a(Au-PeEL)EBL5586319 035 $a(OCoLC)953242144 035 $a(PPN)194378225 035 $a(EXLCZ)993710000000734916 100 $a20160628d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDivergent Series, Summability and Resurgence III$b[electronic resource] $eResurgent Methods and the First Painlevé Equation /$fby Eric Delabaere 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XXII, 230 p. 35 illus., 14 illus. in color.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2155 311 $a3-319-28999-3 327 $aAvant-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. 330 $aThe 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. 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