Divergent series, summability and resurgence.: I, Monodromy and resurgence
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Switzerland : Springer, 2016.
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1 online resource (xxi, 298 pages) : illustrations (some color).
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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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Language:
English
ISBN:
9783319287362, 3319287362
UPC:
10.1007/978-3-319-28736-2

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Bibliography
Includes bibliographical references and index.
Description
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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Citations
APA Citation (style guide)

Mitschi, C., & Sauzin, D. (2016). Divergent series, summability and resurgence. Switzerland, Springer.

Chicago / Turabian - Author Date Citation (style guide)

Mitschi, C and D. Sauzin. 2016. Divergent Series, Summability and Resurgence. Switzerland, Springer.

Chicago / Turabian - Humanities Citation (style guide)

Mitschi, C and D. Sauzin, Divergent Series, Summability and Resurgence. Switzerland, Springer, 2016.

MLA Citation (style guide)

Mitschi, C. and D. Sauzin. Divergent Series, Summability and Resurgence. Switzerland, Springer, 2016.

Note! Citation formats are based on standards as of July 2022. Citations contain only title, author, edition, publisher, and year published. Citations should be used as a guideline and should be double checked for accuracy.
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5050 |6 880-01|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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8808 |6 505-01/(S|a ReferencesPart II Introduction to 1-Summability and Resurgence; Chapter 5 Borel-Laplace Summation; 5.1 Prologue; 5.2 An example by Poincaré; 5.3 The differential algebra C[[z1]]; 5.4 The formal Borel transform and the space of 1-Gevrey formal series C[[z1]]1; 5.5 The convolution in C[[z]] and in C{ζ}; 5.6 The Laplace transform along R+; 5.7 The fine Borel-Laplace summation; 5.8 The Euler series; 5.9 Varying the direction of summation; 5.10 Return to the Euler series; 5.11 The Stirling series; 5.12 Return to Poincaré's example; 5.13 Non-linear operations with 1-summable formal series
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