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On the isoclines of polynomial vector fields
Siberian Mathematical Journal, 1994The author considers autonomous systems (1) \(\dot x = P(x,y)\), \(\dot y = Q(x,y)\) with \(\{P(x,y), Q(x,y)\}\) a polynomial vector field. He proves the following results. Theorem 1. Assume \(P(x,y) = P_m (x,y) + P_n (x,y)\), \(Q(x,y) = Q_m (x,y) + Q_n (x,y)\) with \(m,n > 0\) and \(P_m\), \(Q_m\) and \(P_n\), \(Q_n\) homogeneous polynomials of degree
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Complete polynomial vector fields in a ball
2004Summary: We describe the complete polynomial vector fields in the unit ball of a Euclidean space.
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Poincaré Compactification of Hamiltonian Polynomial Vector Fields
1995There exists an extensive literature on changes of variables which transform the equations of motion of interesting problems in Celestial Mechanics into polynomial form (see [Heg]). In most cases this is achieved by regularizing double collisions or introducing redundant variables, or both.
J. Delgado +3 more
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Local cyclicity in low degree planar piecewise polynomial vector fields
Nonlinear Analysis: Real World Applications, 2021Luiz Fernando Gouveia, Joan Torregrosa
exaly
An efficient method for computing Liouvillian first integrals of planar polynomial vector fields
Journal of Differential Equations, 2021Luiz Duarte, Luis antonio da Mota
exaly
Detecting singular patterns in 2D vector fields using weighted Laurent polynomial
Pattern Recognition, 2012Eraldo Ribeiro
exaly
A New Algorithm for Finding Rational First Integrals of Polynomial Vector Fields
Qualitative Theory of Dynamical Systems, 2010Antoni Ferragut, Hector Giacomini
exaly