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Algebraic structures and invariant manifolds of differential systems

par Figueiredo, Annibal;Rocha Filho, Tarcísio T.M.;Brenig, Léon
Référence Journal of mathematical physics, 39, 5, page (2929-2946)
Publication Publié, 1998-05

Article révisé par les pairs

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Résumé :

Algebraic tools are applied to find integrability properties of ODEs. Bilinear non-associative algebras are associated to a large class of polynomial and nonpolynomial systems of differential equations, since all equations in this class are related to a canonical quadratic differential system: the Lotka-Volterra system. These algebras are classified up to dimension 3 and examples for dimension 4 and 5 are given. Their subalgebras are associated to nonlinear invariant manifolds in the phase space. These manifolds are calculated explicitly. More general algebraic invariant surfaces are also obtained by combining a theorem of Walcher and the Lotka-Volterra canonical form. Applications are given for Lorenz model, Lotka, May-Leonard, and Rikitake systems. © 1998 American Institute of Physics.