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 Deformation Quantization, Gilles Halbout (Ed.) 2 Locally Compact Quantum Groups and Groupoids, Leonid Vainerman (Ed.) From Combinatorics to Dynamical Systems Journe´es de Calcul Formel Strasbourg, March 22Ϫ23, 2002 Editors F. Fauvet C. Mitschi ≥ Walter de Gruyter · Berlin · New York Editors Fre´de´ric Fauvet, UFR de Maths et IRMA Ϫ 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 Ϫ 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 Ϫ 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 SchemeϪ1995: 02.30.Ϫf, 0260.Ϫx, 02.70.Ϫc, 05.45.ϩb, 47.27.Ϫi, 82.40.Ϫg Key words: Multiple zeta values, free Lie algebras, quasi-symmetric functions, irregular singularities, normal forms, mero- morphic connections, ordinary differential equations, Gevrey asymptoticity, differential Galois theory, Lokta- Volterra systems, equation of Kuramoto and Sivashinsky, unidimensional cubic complex equation of Ginzburg and Landau, hybrid automaton and modeling, optimal control, nonlinear ordinary differential equations.