A class of polynomial planar vector fields with polynomial first integral

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other ORP type 01 Oct 2015Embargo end date: 01 Jan 2014 Spain English Publisher:Elsevier BVJournal:Journal of Mathematical Analysis and Applications, volume 430, pages 354-380 (issn: 0022-247X,

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Authors: A. Ferragut; C. Galindo; F. Monserrat;

doi: 10.1016/j.jmaa.2015.04.062 , 10.48550/arxiv.1410.3652

arXiv: 1410.3652

handle: 10234/146328

A class of polynomial planar vector fields with polynomial first integral

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Abstract

We give an algorithm for deciding whether a planar polynomial differential system has a first integral which factorizes as a product of defining polynomials of curves with only one place at infinity. In the affirmative case, our algorithm computes a minimal first integral. In addition, we solve the Poincaré problem for the class of systems which admit a polynomial first integral as above in the sense that the degree of the minimal first integral can be computed from the reduction of singularities of the corresponding vector field.

Country

Spain

Related Organizations

Autonomous University of Barcelona
Spain
Universitat Politècnica de València
Spain
Jaume I University
Spain

Keywords

Blow-up, Invariant algebraic curves, Mathematics - Algebraic Geometry, 34A34, 34C05, 34C08, 14C21, planar polynomial vector field, Classical Analysis and ODEs (math.CA), FOS: Mathematics, invariant algebraic curve, Polynomial first integral, Reduction of singularities, curve with only one place at infinity, Algebraic Geometry (math.AG), Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, reduction of singularities, polynomial first integral, Invariant algebraic curve, Planar polynomial vector field, Mathematics - Classical Analysis and ODEs, Explicit solutions, first integrals of ordinary differential equations, Dynamics induced by flows and semiflows, Curve with only one place at infinity, Symmetries, invariants of ordinary differential equations, MATEMATICA APLICADA, blow-up

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