Algorithmic reduction of Poincaré-Dulac normal forms and Lie algebraic structure (Q5953678)

The main goal of this letter is indeed to combine the Poincaré renormalized forms (PRF) approach with Lie algebraic constructions in order to obtain a procedure that takes a Lie algebra structure and keeps the computational simplicity of the PRF approach. The author deals with a structure which is nongeneric, but relatively common in applications. When this approach is applicable, it is only necessary to solve linear equations and more powerful than the one proposed in previous works [see Symmetry and perturbation theory, Rome 1998, 178-186 (1999; Zbl 1181.37069), Lett. Math. Phys. 42, 103-114 (1997; Zbl 0890.34031), Erratum ibid. 54, 235 (2000; Zbl 0991.37032), Ann. Inst. Henri Poincaré, Phys. Théor. 70, 461-514 (1999; Zbl 0994.34024), Erratum Ann. Henri Poincaré 2, 403 (2001; Zbl 0994.34025)].