Divergent series, summability and resurgence.: I, Monodromy and resurgence
(Web Content)
Author:
Series:
Lecture notes in mathematics (Springer-Verlag) ; volume 2153.
Published:
Switzerland : Springer, 2016.
Format:
Web Content
Content Description:
1 online resource (xxi, 298 pages) : illustrations (some color).
Status:
Available Online
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
Copies
CMU Electronic Access
More Copies In Prospector
Loading Prospector Copies...
Subjects
LC Subjects
OCLC Fast Subjects
More Details
Language:
Unknown
ISBN:
9783319287362, 3319287362
UPC:
10.1007/978-3-319-28736-2
Notes
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
Reviews from GoodReads
Loading GoodReads Reviews.
Citations
APA Citation (style guide)
Mitschi, C., & Sauzin, D. (2016). Divergent series, summability and resurgence. Springer.
Chicago / Turabian - Author Date Citation (style guide)Mitschi, C and D. Sauzin. 2016. Divergent Series, Summability and Resurgence. Springer.
Chicago / Turabian - Humanities Citation (style guide)Mitschi, C and D. Sauzin, Divergent Series, Summability and Resurgence. Springer, 2016.
MLA Citation (style guide)Mitschi, C. and D. Sauzin. Divergent Series, Summability and Resurgence. 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.
Staff View
Grouped Work ID:
5e69c93a-0219-464e-1f80-ba19d08b664b
QR Code
Record Information
| Last Sierra Extract Time | Feb 25, 2025 08:43:32 PM |
|---|---|
| Last File Modification Time | Feb 25, 2025 08:43:51 PM |
| Last Grouped Work Modification Time | Feb 25, 2025 08:43:40 PM |
MARC Record
| LEADER | 06121cam a2200901 i 4500 | ||
|---|---|---|---|
| 001 | 957977143 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
| 007 | cr cnu|||unuuu | ||
| 008 | 160907s2016 sz a ob 001 0 eng d | ||
| 019 | |a 957739709 |a 959592621 | ||
| 020 | |a 9783319287362 |q (electronic bk.) | ||
| 020 | |a 3319287362 |q (electronic bk.) | ||
| 020 | |z 9783319287355 |q (print) | ||
| 020 | |z 3319287354 | ||
| 024 | 7 | |a 10.1007/978-3-319-28736-2 |2 doi | |
| 035 | |a (OCoLC)957977143 |z (OCoLC)957739709 |z (OCoLC)959592621 | ||
| 040 | |a GW5XE |b eng |e rda |e pn |c GW5XE |d YDX |d COO |d STF |d OCLCF |d TJC |d QCL |d OCLCQ |d JG0 |d IOG |d IAD |d JBG |d ICW |d ILO |d ICN |d ESU |d U3W |d KSU |d WYU |d EBLCP |d AUD |d OCLCQ |d AJS |d UKAHL |d OCLCO |d OCLCQ |d S9M |d OCLCL | ||
| 049 | |a COM6 | ||
| 050 | 4 | |a QA295 | |
| 066 | |c (S | ||
| 072 | 7 | |a PBKJ |2 bicssc | |
| 072 | 7 | |a MAT007000 |2 bisacsh | |
| 082 | 0 | 4 | |a 515/.243 |2 23 |
| 084 | |a 34M30 |a 30E15 |a 30B40 |a 34M03 |a 34M40 |a 37F10 |a 34M35 |2 msc | ||
| 100 | 1 | |a Mitschi, C. |q (Claude) |0 https://id.loc.gov/authorities/names/n2003003531 |1 https://id.oclc.org/worldcat/entity/E39PCjFvpQfRvvyc9mJqR4dt4y, |e author. | |
| 245 | 1 | 0 | |a Divergent series, summability and resurgence. |n I, |p Monodromy and resurgence / |c Claude Mitschi, David Sauzin. |
| 246 | 3 | 0 | |a Monodromy and resurgence |
| 264 | 1 | |a Switzerland : |b Springer, |c 2016. | |
| 300 | |a 1 online resource (xxi, 298 pages) : |b illustrations (some color). | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file | ||
| 490 | 1 | |a Lecture notes in mathematics, |x 0075-8434 ; |v 2153 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |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 | ||
| 588 | 0 | |a Online resource; title from PDF title page (SpringerLink, viewed September 7, 2016). | |
| 650 | 0 | |a Divergent series. |0 https://id.loc.gov/authorities/subjects/sh85120240 | |
| 650 | 0 | |a Monodromy groups. |0 https://id.loc.gov/authorities/subjects/sh87005568 | |
| 650 | 6 | |a Séries divergentes. | |
| 650 | 6 | |a Groupes de monodromie. | |
| 650 | 7 | |a Grupos de monodromía. |2 embne | |
| 650 | 7 | |a Divergent series. |2 fast | |
| 650 | 7 | |a Monodromy groups. |2 fast | |
| 700 | 1 | |a Sauzin, D., |d 1966- |0 https://id.loc.gov/authorities/names/n2003001002 |1 https://id.oclc.org/worldcat/entity/E39PCjJGbDJpfTGqg88WdvJdQq, |e author. | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 776 | 0 | 8 | |i Print version: |a Mitschi, C. (Claude). |t Divergent series, summability and resurgence. I, Monodromy and resurgence. |z 3319287354 |z 9783319287355 |w (OCoLC)932095986 |
| 830 | 0 | |a Lecture notes in mathematics (Springer-Verlag) ; |0 https://id.loc.gov/authorities/names/n42015165 |v 2153. |x 0075-8434 | |
| 880 | 8 | |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 | |
| 907 | |a .b51574433 | ||
| 948 | |a MARCIVE Overnight, in 2024.04 | ||
| 948 | |a MARCIVE Overnight, in 2023.01 | ||
| 948 | |a MARCIVE Over, 07/2021 | ||
| 948 | |a MARCIVE Comp, 2019.12 | ||
| 948 | |a MARCIVE Comp, 2018.05 | ||
| 948 | |a MARCIVE August, 2017 | ||
| 948 | |a MARCIVE extract Aug 5, 2017 | ||
| 989 | |1 .i151462781 |d cueme |g - |m |h 0 |x 0 |t 0 |i 0 |j 200 |k 240404 |o - |w Springer Nature |u http://ezproxy.coloradomesa.edu/login?url=https://link.springer.com/10.1007/978-3-319-28736-2 | ||
| 994 | |a 92 |b COM | ||
| 995 | |a Loaded with m2btab.ltiac in 2024.04 | ||
| 995 | |a Loaded with m2btab.elec in 2024.04 | ||
| 995 | |a Loaded with m2btab.ltiac in 2023.01 | ||
| 995 | |a Loaded with m2btab.ltiac in 2021.07 | ||
| 995 | |a Loaded with m2btab.elec in 2021.06 | ||
| 995 | |a Loaded with m2btab.ltiac in 2019.12 | ||
| 995 | |a Loaded with m2btab.ltiac in 2018.06 | ||
| 995 | |a Loaded with m2btab.ltiac in 2017.09 | ||
| 995 | |a Loaded with m2btab.elec in 2016 | ||
| 995 | |a Loaded with m2btab.elec in 2016 | ||
| 995 | |a Loaded with m2btab.elec in 2016 | ||
| 995 | |a OCLC offline update by CMU | ||
| 998 | |a (3)cue |a cu |b 240404 |c m |d z |e - |f eng |g sz |h 0 |i 2 | ||
| 998 | |e - |f eng |a cue |a cu | ||
| 999 | |e z | ||
| 999 | |a cue | ||