Vector Fields, Invariant Varieties and Linear Systems

Details Vector Fields, Invariant Varieties and Linear Systems Vector Fields, Invariant Varieties and Linear Systems

2000-11-24

arxiv.org/abs/math/0011205v1

Annales de L'Institut Fourier, 51 no.5, pp.1385-1405, 2001.

Mathematics

Dynamical Systems

15 pages, Latex

Scientific paper

We investigate the interplay between invariant varieties of vector fields and the inflection locus of linear systems with respect to the vector field. Among the consequences of such investigation we obtain a computational criteria for the existence of rational first integrals of a given degree, bounds for the number of first integrals on families of vector fields and a generalization of Darboux's criteria. We also provide a new proof of Gomez-Mont's result on foliations with all leaves algebraic.

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