Complete polynomial vector fields on \C², Part I

2002/10/24 by Julio C. Rebelo, Rebelo, Julio C.
Mathematics · #32J15 #32M25 #34A20 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:32J15 #msc:32M25 #msc:34A20

paper · pdf · doi:10.48550/arxiv.math/0210392

33 pages

arxiv created 2002/10/24 · arxiv updated 2009/11/30

Abstract

In this work, under a mild assumption, we give the classification of the complete polynomial vector fields in two variables up to algebraic automorphisms of \C². The general problem is also reduced to the study of the combinatorics of certain resolutions of singularities. Whereas we deal with \C-complete vector fields, our results also apply to \R-complete ones thanks to a theorem of Forstneric \citeforst.

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