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Divergent series, summability and re...

Mitschi, Claude.

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Divergent series, summability and resurgence.. I,. Monodromy and resurgence

Record Type:	Electronic resources : Monograph/item
Title/Author:	Divergent series, summability and resurgence./ by Claude Mitschi, David Sauzin.
remainder title:	Monodromy and resurgence
Author:	Mitschi, Claude.
other author:	Sauzin, David.
Published:	Cham :Springer International Publishing : : 2016.,
Description:	xxi, 298 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Divergent series. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-28736-2
ISBN:	9783319287362

Divergent series, summability and resurgence.. I,. Monodromy and resurgence
Mitschi, Claude.

Divergent series, summability and resurgence.I,Monodromy and resurgence[electronic resource] /Monodromy and resurgenceby Claude Mitschi, David Sauzin. - Cham :Springer International Publishing :2016. - xxi, 298 p. :ill. (some col.), digital ;24 cm. - Lecture notes in mathematics,21530075-8434 ;. - Lecture notes in mathematics ;2046..

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.

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.

ISBN: 9783319287362

Standard No.: 10.1007/978-3-319-28736-2doiSubjects--Topical Terms:

728335
Divergent series.

LC Class. No.: QA295

Dewey Class. No.: 515.243

Divergent series, summability and resurgence.. I,. Monodromy and resurgence
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505 0 $a 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.
520 $a 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.
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650 2 4 $a Sequences, Series, Summability. $3 897266
650 2 4 $a Difference and Functional Equations. $3 897290
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 891276
650 2 4 $a Topological Groups, Lie Groups. $3 891005
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