Download PDF by F. Fauvet, C. Mitschi: From Combinatorics to Dynamical Systems: Journees de Calcul

By F. Fauvet, C. Mitschi

ISBN-10: 3110178753

ISBN-13: 9783110178753

9 examine papers from a March 2002 convention make clear numerous parts of combinatorics and dynamical structures, with desktop algebra as an underlying and unifying subject matter. subject matters coated are abnormal connections, rank relief and summability of options of differential platforms, asymptotic habit of divergent sequence, integrability of Hamiltonian structures, a number of zeta values, quasi polynomial formalism, Padè approximants with regards to analytic integrability, and hybrid platforms. The booklet should be of curiosity to mathematicians and theoretical physicists. there's no topic index.

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Additional resources for From Combinatorics to Dynamical Systems: Journees de Calcul Formel, Strasbourg, March 22-23, 2002

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Let k1 , . . , km denote the distinct elementary divisors of M in their respective multiplicities. Let K denote the diagonal matrix and n1 , . . , nm K = diag(k1 In1 , . . , km Inm ). Let (e) be a Smith basis of with respect to M, and (ε) the basis zK (e) of M. Let further A = Mat(∇θ , (e)) = A−p z−p + · · · and B = Mat(∇θ , (ε)) = B−p z−p + · · · be the respective matrices of ∇θ in the given bases. e. element-wise Bij = Aij zkj −ki − δij ki . −p hence if kj − ki < 0 implies v(Aij ) > −p. By assumption, we have v(Bij ) Thus, the matrix A−p has a block upper-triangular structure matching the blocks of the matrix K.

Wt ) of V such that is adapted to W . We call 32 Eduardo Corel W = (W1 , . . , Wt ) the Sibuya splitting of ∇ according to . Moreover, to the direct sum W . is adapted The lattice admits bases which respect the direct sum V = W1 ⊕ · · · ⊕ Wt , which we will call Sibuya bases of . 19. Let ∇θ = ∇θr + ϕ be the canonical decomposition attached to the connection ∇. Let V1 , . . , Vs denote the eigenspaces of the determinant map ϕ and Sp(ϕ) = {ϕ1 , . . , ϕs } the distinct determinant factors of ∇.

B) since [D−k , B˜ 0 ] = [T −1 B−k T , T −1 B0 T ] = 0 for all k = 1, . . , p. There is a gauge P such that B˜ [P ] = A. 11 shows that the gauge P satisfies conditions the gauge P applied to B. (Cp−1 ). Equation (p) is then given in B-blocks as (0) (0) −1 AI I = PI I (0) (0) B˜ I I PI I and (0) (0) −1 AI J = PI I (0) (0) (0) B˜ I J PJ J + PI I −1 (q− ) PI J (−p+ ) λI (−p+ ) − λJ Algorithmic computation of exponents for linear differential systems 49 (−p+ ) (−p+ ) − λJ = 0.

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From Combinatorics to Dynamical Systems: Journees de Calcul Formel, Strasbourg, March 22-23, 2002 by F. Fauvet, C. Mitschi

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