Divergent Series, Summability and Resurgence III - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Divergent Series, Summability and Resurgence III write by Eric Delabaere. This book was released on 2016-06-28. Divergent Series, Summability and Resurgence III available in PDF, EPUB and Kindle. The aim of this volume is two-fold. First, to show how the resurgent methods introduced in volume 1 can be applied efficiently in a non-linear setting; to this end further properties of the resurgence theory must be developed. Second, to analyze the fundamental example of the First Painlevé equation. The resurgent analysis of singularities is pushed all the way up to the so-called “bridge equation”, which concentrates all information about the non-linear Stokes phenomenon at infinity of the First Painlevé equation. The third in a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists who are interested in divergent power series and related problems, such as the Stokes phenomenon. The prerequisites are a working knowledge of complex analysis at the first-year graduate level and of the theory of resurgence, as presented in volume 1.
Divergent Series, Summability and Resurgence II
Divergent Series, Summability and Resurgence II - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Divergent Series, Summability and Resurgence II write by Michèle Loday-Richaud. This book was released on 2016-06-28. Divergent Series, Summability and Resurgence II available in PDF, EPUB and Kindle. Addressing the question how to “sum” a power series in one variable when it diverges, that is, how to attach to it analytic functions, the volume gives answers by presenting and comparing the various theories of k-summability and multisummability. These theories apply in particular to all solutions of ordinary differential equations. The volume includes applications, examples and revisits, from a cohomological point of view, the group of tangent-to-identity germs of diffeomorphisms of C studied in volume 1. With a view to applying the theories to solutions of differential equations, a detailed survey of linear ordinary differential equations is provided, which includes Gevrey asymptotic expansions, Newton polygons, index theorems and Sibuya’s proof of the meromorphic classification theorem that characterizes the Stokes phenomenon for linear differential equations. This volume is the second in a series of three, entitled Divergent Series, Summability and Resurgence. It is aimed at graduate students and researchers in mathematics and theoretical physics who are interested in divergent series, Although closely related to the other two volumes, it can be read independently.
Divergent Series, Summability and Resurgence I
Divergent Series, Summability and Resurgence I - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Divergent Series, Summability and Resurgence I write by Claude Mitschi. This book was released on 2016-08-27. Divergent Series, Summability and Resurgence I available in PDF, EPUB and Kindle. 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.
Divergent Series, Summability and Resurgence
Divergent Series, Summability and Resurgence - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Divergent Series, Summability and Resurgence write by . This book was released on 2016. Divergent Series, Summability and Resurgence available in PDF, EPUB and Kindle.
Divergent Series, Summability and Resurgence I-III
Divergent Series, Summability and Resurgence I-III - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Divergent Series, Summability and Resurgence I-III write by Eric Delabaere. This book was released on 2017-09. Divergent Series, Summability and Resurgence I-III available in PDF, EPUB and Kindle. This three-volume work treats divergent series in one variable, especially those arising as solutions to complex ordinary differential or difference equations, and methods for extracting their analytic information. It provides a systematic construction, illustrated with examples, of the various theories of summability and the theory of resurgence developed since the 1980s. The Stokes phenomenon, for both linear and non-linear equations, plays an underlying and unifying role throughout the volumes. Applications presented include resurgent analyses of the First Painlevé equation and of the tangent-to-identity germs of diffeomorphisms of C, and links to differential Galois theory and the Riemann-Hilbert problem for linear differential equations. The volumes are aimed at graduate students, mathematicians in general, and theoretical physicists who are interested in the theories of monodromy, summability, and resurgence, as well as the current problems in the field.Although the three volumes are closely related, they have been organized to be read independently. The prerequisites are advanced calculus, especially holomorphic functions in one complex variable, and differential algebra. Moreover; the various themes are presented thoroughly step-by-step so as to be accessible to first-year graduate students in mathematics. This three-volume treatise should become a reference on summability and resurgence.
