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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Melanocytes

,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

Adherent

,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

DUST

enormous

,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

天然熱噴泉

,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

天然熱噴泉

Derogate

,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.

irritation

陰謀