Divergent Series, Summability and Resurgence I Monodromy and Resurge
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 monod
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Claude Mitschi David Sauzin
Divergent Series, Summability and Resurgence I Monodromy and Resurgence
Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Camillo De Lellis, Zü rich Mario di Bernardo, Bristol Alessio Figalli, Austin Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gábor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, Paris and New York Catharina Stroppel, Bonn Anna Wienhard, Heidelberg
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Claude Mitschi • David Sauzin
Divergent Series, Summability and Resurgence I Monodromy and Resurgence
Claude Mitschi Inst. de Recherche Mathématique Avancée Université de Strasbourg et CNRS Strasbourg, France
David Sauzin CNRS UMR 8028 -- IMCCE Observatoire de Paris Paris, France
ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-3-319-28735-5 ISBN 978-3-319-28736-2 (eBook) DOI 10.1007/978-3-319-28736-2 Library of Congress Control Number: 2016940058 Mathematics Subject Classification (2010): 34M30, 30E15, 30B40, 34M03, 34M40, 37F10, 34M35
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a` la m´emoire d’Andrey Bolibrukh, C.M.
a` Lili, D.S.
Avant-Propos
Le sujet principal trait´e dans la s´erie de volumes Divergent Series, Summability and Resurgence est la th´eorie des d´eveloppements asymptotiques et des s´eries divergentes appliqu´ee aux e´ quations diff´erentielles ordinaires (EDO) et a` certaines e´ quations aux diff´erences dans le champ complexe. Les e´ quations diff´erentielles dans le champ complexe, et dans le cadre holomorphe, sont un sujet tr`es ancien. La th´eorie a e´ t´e tr`es active dans la deuxi`eme moiti´e du XIX-`eme si`ecle. En ce qui concerne les e´ quations
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