Topics covered include irregular connections, rank reduction and summability of solutions of differential systems, asymptotic behaviour of divergent series, integrability of Hamiltonian systems, multiple zeta values, quasi-polynomial formalism, Padé approximants related to analytic integrability, hybrid systems.
The interactions between computer algebra, dynamical systems and combinatorics discussed in this volume should be useful for both mathematicians and theoretical physicists who are interested in effective computation.
IRMA Lectures in Mathematics and Theoretical Physics 3 Edited by Vladimir G. Turaev Institut de Recherche Mathe´matique Avance´e Universite´ Louis Pasteur et CNRS 7 rue Rene´ Descartes 67084 Strasbourg Cedex France IRMA Lectures in Mathematics and Theoretical Physics 1 2 Deformation Quantization, Gilles Halbout (Ed.) Locally Compact Quantum Groups and Groupoids, Leonid Vainerman (Ed.) From Combinatorics to Dynamical Systems Journe´es de Calcul Formel Strasbourg, March 22⫺23, 2002 Editors F. Fauvet C. Mitschi ≥ Walter de Gruyter · Berlin · New York Editors Fre´de´ric Fauvet, UFR de Maths et IRMA ⫺ CNRS UMR 7501, Universite´ Louis Pasteur, 7, rue Rene´ Descartes, 67084 Strasbourg Cedex, France, e-mail:
[email protected] Claude Mitschi UFR de Maths et IRMA ⫺ CNRS UMR 7501, Universite´ Louis Pasteur, 7, rue Rene´ Descartes, 67084 Strasbourg Cedex, France, e-mail:
[email protected] Series Editor Vladimir G. Turaev Institut de Recherche Mathe´matique Avance´e (IRMA), Universite´ Louis Pasteur ⫺ C.N.R.S., 7, rue Rene´ Descartes, 67084 Strasbourg Cedex, France, e-mail:
[email protected] Mathematics Subject Classification 2000: 11-04; 05E99, 11M99, 12H05, 12H10, 32C38, 33E05, 34A25, 34A30, 34A34, C20, 34E05, 34E10, 34M25, 34M30, 34M35, 40A05, 40D05, 68W30, 70F07, 70H05, 70H06 Physics and Astronomy Classification Scheme⫺1995: 02.30.⫺f, 0260.⫺x, 02.70.⫺c, 05.45.⫹b, 47.27.⫺i, 82.40.⫺g Key words: Multiple zeta values, free Lie algebras, quasi-symmetric functions, irregular singularities, normal forms, meromorphic connections, ordinary differential equations, Gevrey asymptoticity, differential Galois theory, LoktaVolterra systems, equation of Kuramoto and Sivashinsky, unidimensional cubic complex equation of Ginzburg and Landau, hybrid automaton and modeling, optimal control, nonlinear ordinary differential equations. 앝 Printed on acid-free paper which falls within the guidelines of the ANSI 앪 to ensure permanence and durability. Library of Congress Cataloging-in-Publication Data From combinatorics to dynamical systems : journe´es de calcul formel, Strasbourg, March 22⫺23, 2002 / editors F. Fauvet, C. Mitschi. p. cm. ⫺ (IRMA lectures in mathematics and theoretical physics ; 3) Includes bibliographical references. ISBN 3-11-017875-3 (alk. paper) 1. Algebra ⫺ Data Processing ⫺ Congresses. I. Fauvet, F. (Fre´de´ric). II. Mitschi, C. (Claude). III. Series. QA155.7.E4F76 2003 512⫺dc22 2003062471 ISBN 3-11-017875-3 Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at ⬍http://dnb.ddb.de⬎. 쑔