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Search: MSC category 37F75 ( Holomorphic foliations and vector fields [See also 32M25, 32S65, 34Mxx] )

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1. CJM 2002 (vol 54 pp. 897)

Fortuny Ayuso, Pedro
The Valuative Theory of Foliations
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.

Categories:12J20, 13F30, 16W60, 37F75, 34M25

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