Divergent Series, Summability and Resurgence III: Resurgent Methods and the First Painlevé Equation
Springer | Analysis | Jun 29 2016 | ISBN-10: 3319289993 | 230 pages | pdf | 2.39 mb
Authors: Delabaere, Eric
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 Stokes phenomena of Painlevé I are made explicit by means of the so-called bridge equation
The 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 1.
Number of Illustrations and Tables
21 b/w illustrations, 14 illustrations in colour
Sequences, Series, Summability
Ordinary Differential Equations
Functions of a Complex Variable