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Divergent series, summability and re...

Mitschi, Claude.

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

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Divergent series, summability and resurgence./ by Claude Mitschi, David Sauzin.
其他題名:	Monodromy and resurgence
作者:	Mitschi, Claude.
其他作者:	Sauzin, David.
出版者:	Cham :Springer International Publishing : : 2016.,
面頁冊數:	xxi, 298 p. :ill. (some col.), digital ;24 cm.
內容註:	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
標題:	Divergent series. -
電子資源:	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

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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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