Displaying similar documents to “Basic algebro-geometric conceps in the study of planar polynomial vector fields.”

Nondegenerate linearizable centre of complex planar quadratic and symmetric cubic systems in C.

Colin Christopher, Christiane Rousseau (2001)

Publicacions Matemàtiques

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In this paper we consider complex differential systems in the plane, which are linearizable in the neighborhood of a nondegenerate centre. We find necessary and sufficient conditions for linearizability for the class of complex quadratic systems and for the class of complex cubic systems symmetric with respect to a centre. The sufficiency of these conditions is shown by exhibiting explicitly a linearizing change of coordinates, either of Darboux type or a generalization of it. ...

Curves in P(C) with 1-dimensional symmetry.

A. A. du Plessis, Charles Terence Clegg Wall (1999)

Revista Matemática Complutense

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In a previous paper we showed that the existence of a 1-parameter symmetry group of a hypersurface X in projective space was equivalent to failure of versality of a certain unfolding. Here we study in detail (reduced) plane curves of degree d ≥ 3, excluding the trivial case of cones. We enumerate all possible group actions -these have to be either semisimple or unipotent- for any degree d. A 2-parameter group can only occur if d = 3. Explicit lists of singularities of the corresponding...

Vector fields, invariant varieties and linear systems

Jorge Vitório Pereira (2001)

Annales de l’institut Fourier

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We investigate the interplay between invariant varieties of vector fields and the inflection locus of linear systems with respect to the vector field. Among the consequences of such investigation we obtain a computational criterion for the existence of rational first integrals of a given degree, bounds for the number of first integrals on families of vector fields, and a generalization of Darboux's criteria. We also provide a new proof of Gomez--Mont's result...