Transseries And Real Differential Algebra

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Transseries are formal objects constructed from an infinitely large variable x and the reals using infinite summation, exponentiation and logarithm. They are suitable for modeling "strongly monotonic" or "tame" asymptotic solutions to differential equations and find their origin in at least three different areas of mathematics: analysis, model theory and computer algebra. They play a crucial role in Écalle's proof of Dulac's conjecture, which is closely related to Hilbert's 16th problem. The aim of the present book is to give a detailed and self-contained exposition of the theory of transseries, in the hope of making it more accessible to non-specialists.


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Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris 1888 J. van der Hoeven Transseries and Real Differential Algebra ABC Author Joris van der Hoeven Département de Mathématiques, CNRS Université Paris-Sud Bâtiment 425 91405 Orsay CX France e-mail: [email protected] Library of Congress Control Number: 2006930997 Mathematics Subject Classification (2000): 34E13, 03C65, 68w30, 34M35, 13H05 ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISBN-10 3-540-35590-1 Springer Berlin Heidelberg New York ISBN-13 978-3-540-35590-8 Springer Berlin Heidelberg New York DOI 10.1007/3-540-35590-1 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the
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