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OverviewProviding 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. Full Product DetailsAuthor: Claude Mitschi , David SauzinPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 1st ed. 2016 Volume: 2153 Dimensions: Width: 15.50cm , Height: 1.70cm , Length: 23.50cm Weight: 4.861kg ISBN: 9783319287355ISBN 10: 3319287354 Pages: 298 Publication Date: 28 August 2016 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand We will order this item for you from a manufactured on demand supplier. Table of ContentsReviewsThe book is the first of three independent books whose aim is to describe methods of the analytic theory of differential equations such as monodromy, analytic continuation, resurgence, summability etc. It is aimed at graduate students, mathematicians and theoretical physicists. (Vladimir P. Kostov, zbMATH 1355.34003, 2017) Author InformationTab Content 6Author Website:Countries AvailableAll regions |