Divergent Series, Summability and Resurgence III Resurgent Methods a
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 funda
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Eric Delabaere
Divergent Series, Summability and Resurgence III Resurgent Methods and the First Painlevé Equation
Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Camillo De Lellis, Zurich Mario di Bernardo, Bristol Alessio Figalli, Austin Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gabor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, Paris and New York Catharina Stroppel, Bonn Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Eric Delabaere
Divergent Series, Summability and Resurgence III Resurgent Methods and the First Painlevé Equation
Eric Delabaere Département de Mathématiques Université d’Angers Angers, France
ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-3-319-28999-1 ISBN 978-3-319-29000-3 (eBook) DOI 10.1007/978-3-319-29000-3 Library of Congress Control Number: 2016940058
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To my children Dana´e and Adrian, to my wife Fabienne.
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 lin´eaires, les math´ematiciens de cette e´ poque les ont subdivis´ees en deux classes. Pour la premi`ere, celle des e´ quations a` points singuliers r´eguliers (ou de
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