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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.
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.
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
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.
| Erscheinungsjahr: | 2016 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 320 |
| Reihe: | Lecture Notes in Mathematics |
| Inhalt: |
xxi
298 S. 5 s/w Illustr. 19 farbige Illustr. 298 p. 24 illus. 19 illus. in color. |
| ISBN-13: | 9783319287355 |
| ISBN-10: | 3319287354 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-28735-5 |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Sauzin, David
Mitschi, Claude |
| Auflage: | 1st ed. 2016 |
| Hersteller: |
Springer International Publishing
Springer International Publishing AG Lecture Notes in Mathematics |
| Maße: | 235 x 155 x 18 mm |
| Von/Mit: | David Sauzin (u. a.) |
| Erscheinungsdatum: | 28.08.2016 |
| Gewicht: | 0,487 kg |
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
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.
| Erscheinungsjahr: | 2016 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 320 |
| Reihe: | Lecture Notes in Mathematics |
| Inhalt: |
xxi
298 S. 5 s/w Illustr. 19 farbige Illustr. 298 p. 24 illus. 19 illus. in color. |
| ISBN-13: | 9783319287355 |
| ISBN-10: | 3319287354 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-28735-5 |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Sauzin, David
Mitschi, Claude |
| Auflage: | 1st ed. 2016 |
| Hersteller: |
Springer International Publishing
Springer International Publishing AG Lecture Notes in Mathematics |
| Maße: | 235 x 155 x 18 mm |
| Von/Mit: | David Sauzin (u. a.) |
| Erscheinungsdatum: | 28.08.2016 |
| Gewicht: | 0,487 kg |
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