03231cmm a2200457 i 4500991003409249707536cr cn ---mpcbr170809s2016 de | o j |||| 0|eng d978331928736210.1007/978-3-319-28736-2doib14329347-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng515.35223AMS 40-02Mitschi, Claude730104Divergent series, summability and resurgence I[e-book] :Monodromy and resurgence /by Claude Mitschi, David SauzinCham :Springer,20161 online resourcetexttxtrdacontentcomputercrdamediaonline resourcecrrdacarrierLecture Notes in Mathematics,0075-8434 ;2153Preface ; 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 ; IndexProviding 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 algebraTopological groupsLie groupsDifference equationsFunctional equationsDynamicsErgodic theoryDifferential equationsSequences (Mathematics)Sauzin, Davidauthorhttp://id.loc.gov/vocabulary/relators/aut730103SpringerLink (Online service)Printed edition:9783319287355https://link.springer.com/book/10.1007/978-3-319-28736-2An electronic book accessible through the World Wide Web.b1432934703-03-2209-08-17991003409249707536Divergent series, summability and resurgence I1748345UNISALENTOle01309-08-17m@ -engde 00