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The Valuative Theory of Foliations

Published online by Cambridge University Press:  20 November 2018

Pedro Fortuny Ayuso
Pedro Fortuny Ayuso*
Affiliation:
School of Mathematical Sciences, Queen Mary College, University of London, Mile End Road, London E1 4NS UK, email: [email protected]
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Abstract

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This paper gives a characterization of valuations that follow the singular infinitely near points of plane vector fields, using the notion of L'Hôpital 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.

Keywords

12J2013F3016W6037F7534M25
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 54 , Issue 5 , 01 October 2002 , pp. 897 - 915
Copyright
Copyright © Canadian Mathematical Society 2002

References

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