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Divergent Series, Summability and Resurgence I, 1st ed. 2016 Monodromy and Resurgence Lecture Notes in Mathematics Series, Vol. 2153

Langue : Anglais

Auteurs :

Couverture de l’ouvrage Divergent Series, Summability and Resurgence I
Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential equations, their formal solutions at singular points, their monodromy and their differential Galois groups. The Riemann-Hilbert problem is discussed from Bolibrukh?s point of view.
The second part expounds 1-summability and Ecalle?s theory of resurgence under fairly general conditions. It contains numerous examples and presents an analysis of the singularities in the Borel plane via ?alien calculus?, which provides a full description of the Stokes phenomenon for linear or non-linear differential or difference equations.
The first of a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists interested in geometric, algebraic or local analytic properties of dynamical systems. It includes useful exercises with solutions. The prerequisites are a working knowledge of elementary complex analysis and differential algebra.

Preface.-Preface to the three volumes.- Part I:Monodromy in Linear Differential Equations.- 1 analytic continuation and monodromy.- Differential Galois Theory.- Inverse Problems.- The Riemann-Hilbert problem.- Part II: Introduction to 1-Summability and Resurgence.- 5 Borel-Laplace Summation.- Resurgent Functions and Alien Calculus.- the Resurgent Viewpoint on Holomorphic Tangent-to-Identity Germs.- Acknowledgements.- Index.

Features an elementary, self-contained introduction to analytic differential Galois theory and the Riemann-Hilbert problem

Provides a foundation that will allow the reader to independently explore and understand the specialized literature in the field

Focuses on 1-summability and resurgence, with a view to nonlinear problems

For the first time, resurgence theory is introduced with great pedagogical care and the main proofs are given in full detail

All notions are motivated and illustrated by numerous examples and applications

Date de parution :

Ouvrage de 298 p.

15.5x23.5 cm

Disponible chez l'éditeur (délai d'approvisionnement : 15 jours).

Prix indicatif 52,74 €

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