Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Resurgent methods and the first Painlevé equation

Abstract : The paper is and extended form of a course given at a CIMPA master class held in LIMA, Perù, in the summer of 2008. It aims at showing the resurgent methods acting on an example and, along that line, to extend the presentation of the resurgence theory of Jean Ecalle provided that the need. The example that we follow along this paper is the first Painlevé differential equation. Among various results, we detail the formal transform that brings Painlevé I to its normal form and we analyze its 1-summability. The complete resurgent structure is eventually shown for Painlevé I, as an upshot from the resurgence theory. The paper is self-contained and essentially aims at graduate students.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-01067086
Contributor : Eric Delabaere <>
Submitted on : Monday, September 22, 2014 - 7:08:01 PM
Last modification on : Friday, May 10, 2019 - 12:14:02 PM
Long-term archiving on: : Friday, April 14, 2017 - 1:46:30 PM

File

book-Perou-ED.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01067086, version 1

Collections

Citation

Eric Delabaere. Resurgent methods and the first Painlevé equation. 2014. ⟨hal-01067086v1⟩

Share

Metrics

Record views

432

Files downloads

619