From Combinatorics to Dynamical Systems
This is the proceedings of the conference “Journées de calcul formel en l'honneur de Jean Thomann”, which took place at IRMA (Institut de Recherche Mathématique Avancée) in Strasbourg in March 2003. The meeting was devoted to dynamical systems, computer algebra, and theoretical physics. The first paper, by M. Espie, J.-C. Novelli and G. Racinet, contains computations of certain graded Lie algebras related to multiple zeta values. The article by E. Corel gives an algebraic and algorithmic treatment of formal exponents at an irregular singularity. The article by J. L. Martins studies irregular meromorphic connections in higher dimensions. The paper by M. A. Barkatou, F. Chyzak and M. Loday-Richaud describes various algorithms for the rank reduction of differential systems. The article by M. Canalis-Durand presents a “pattern recognition algorithm” for Gevrey power series. The article by D. Boucher and J.-A. Weil gives a new proof of the non-integrability of the planar three-body problem. The paper by L. Brenig uses the Quasi Polynomial formalism to obtain effective integrability for some dynamical systems. The article by R. Conte, M. Musete and T.-L. Yee, presents an example of an analytical trajectory in a chaotic system. The last article, by J. Della Dora and M. Mirica-Ruse, presents formalization for the concept of a hybrid system.