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The Valuative Theory of Foliations |
Canad. J. Math. 54(2002), 897-915
Published:2002-10-01
Printed: Oct 2002
Printed: Oct 2002
- Pedro Fortuny Ayuso
Abstract
This paper gives a characterization of valuations that follow the
singular infinitely near points of plane vector fields, using the
notion of L'H\^opital 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.
| MSC Classifications: |
12J20 - General valuation theory [See also 13A18] 13F30 - Valuation rings [See also 13A18] 16W60 - Valuations, completions, formal power series and related constructions [See also 13Jxx] 37F75 - Holomorphic foliations and vector fields [See also 32M25, 32S65, 34Mxx] 34M25 - Formal solutions, transform techniques |