Displaying similar documents to “On different in orders in an algebraic number field and special units connected with it”

Liouvillian first integrals of homogeneouspolynomial 3-dimensional vector fields

Jean Moulin Ollagnier (1996)

Colloquium Mathematicae

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Given a 3-dimensional vector field V with coordinates V x , V y and V z that are homogeneous polynomials in the ring k[x,y,z], we give a necessary and sufficient condition for the existence of a Liouvillian first integral of V which is homogeneous of degree 0. This condition is the existence of some 1-forms with coordinates in the ring k[x,y,z] enjoying precise properties; in particular, they have to be integrable in the sense of Pfaff and orthogonal to the vector field V. Thus, our theorem...