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The Valuative Theory of Foliations

  Published:2002-10-01
 Printed: Oct 2002
  • Pedro Fortuny Ayuso
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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, 13F30, 16W60, 37F75, 34M25 show english descriptions General valuation theory [See also 13A18]
Valuation rings [See also 13A18]
Valuations, completions, formal power series and related constructions [See also 13Jxx]
Holomorphic foliations and vector fields [See also 32M25, 32S65, 34Mxx]
Formal solutions, transform techniques
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
 

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