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Titlebook: Divergent Series, Summability and Resurgence III; Resurgent Methods an Eric Delabaere Book 2016 The Editor(s) (if applicable) and The Autho

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发表于 2025-3-21 19:08:33 | 显示全部楼层 |阅读模式
书目名称Divergent Series, Summability and Resurgence III
副标题Resurgent Methods an
编辑Eric Delabaere
视频video
概述Features a thorough resurgent analysis of.the celebrated non-linear differential equation Painlevé I.Includes new specialized results in the.theory of resurgence.For the first time, higher order Stoke
丛书名称Lecture Notes in Mathematics
图书封面Titlebook: Divergent Series, Summability and Resurgence III; Resurgent Methods an Eric Delabaere Book 2016 The Editor(s) (if applicable) and The Autho
描述The aim of this volume is two-fold. First, to show howthe resurgent methods introduced in volume 1 can be applied efficiently in anon-linear setting; to this end further properties of the resurgence theorymust be developed. Second, to analyze the fundamental example of the FirstPainlevé equation. The resurgent analysis of singularities is pushed all theway up to the so-called “bridge equation”, which concentrates allinformation about the non-linear Stokes phenomenon at infinity of the First Painlevéequation. ..The third in a series of three, entitled .Divergent Series, Summability andResurgence., this volume is aimed at graduate students, mathematicians andtheoretical physicists who are interested in divergent power series and relatedproblems, such as the Stokes phenomenon. The prerequisites are a workingknowledge of complex analysis at the first-year graduate level and of thetheory of resurgence, as presented in volume 1. 
出版日期Book 2016
关键词34Mxx,34M30,40Cxx,35Q15,34M50,30B40,30D05,37Fxx,37F99,34M55; Divergent Series; Summability; Resurgence;
版次1
doihttps://doi.org/10.1007/978-3-319-29000-3
isbn_softcover978-3-319-28999-1
isbn_ebook978-3-319-29000-3Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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发表于 2025-3-21 23:04:41 | 显示全部楼层
,The First Painlevé Equation,é equation is recalled (Sect. 2.1). We precise how the Painlevé property translates for the first Painlevé equation (Sect. 2.2), a proof of which being postponed to an appendix. We explain how the first Painlevé equation also arises as a condition of isomonodromic deformations for a linear ODE (Sect
Melanocytes
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发表于 2025-3-22 01:32:35 | 显示全部楼层
,Tritruncated Solutions For The First Painlevé Equation,ect. 2.6. This example will introduce the reader to common reasonings in resurgence theory. We construct a prepared form associated with the first Painlevé equation (Sec 3.1). This prepared ODE has a unique formal solution from which we deduce the existence of truncated solutions by application of t
Adherent
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DUST
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发表于 2025-3-22 09:57:10 | 显示全部楼层
,Transseries And Formal Integral For The First Painlevé Equation,th the first Painlevé equation, which will be used later on to get the truncated solutions : this is done in Sect. 5.3, after some preliminaries in Sect. 5.1 and Sect. 5.2. Our second goal is to build the formal integral for the first Painlevé equation and, equivalently, the canonical normal form eq
enormous
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发表于 2025-3-22 14:01:18 | 显示全部楼层
,Truncated Solutions For The First Painlevé Equation,, we show that formal series components of the formal integral are 1-Gevrey and their minors have analytic properties quite similar to those for the minor of the formal series solution we started with (Sect. 6.1). We then make a focus on the transseries solution and we show their Borel-Laplace summa
天然热喷泉
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天然热喷泉
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发表于 2025-3-22 23:21:47 | 显示全部楼层
,Resurgent Structure For The First Painlevé Equation,t structure is given in Sect. 8.1. Its proof is given using the so-called bridge equation (Sect. 8.4), after some preliminaries (Sect. 8.3). The nonlinear Stokes phenomena are briefly analyzed in Sect. 8.2.
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irritation
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