The Valuative Theory Of Foliations

This paper gives a characterization of valuations which follow the singular infinitely near points of plane vector fields, using the notion of L'Hopital valuation, which generalizes a well known classical condition. With that tool, we give a valuative description of vector fields with infinite solutions, singularities with rational quotient of eigenvalues in its linear part, and polynomial vector fields with transcendental solutions, among other results