Algorithmic reduction of Poincare'-Dulac normal forms and Lie algebraic structure

Details Algorithmic reduction of Poincare'-Dulac normal forms and Lie algebraic structure Algorithmic reduction of Poincare'-Dulac normal forms and Lie algebraic structure

2001-02-28

arxiv.org/abs/math-ph/0102037v1

Lett. Math. Phys. 57 (2001), 41-60

Physics

Mathematical Physics

20 pages, no figures

Scientific paper

The Poincare'-Dulac normal form of a given resonant system is in general non unique; given a specific normal form, one would like to further reduce it to a simplest normal form. In this note we give an algorithm, based on the Lie algebraic structure of the set of normal forms, to obtain this. The algorithm can be applied under some condition, non generic but often met in applications; when applicable, it only requires to solve linear equations, and is more powerful than the one proposed in previous work by the same author [Lett. Math. Phys. 42, 103-114; and Ann. I.H.P. 70, 461-514].

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