A note on the completeness of homogeneous quadratic vector fields on the plane
Copyright policy )A note on the completeness of homogeneous quadratic vector fields on the plane
The authors give a full description of the complete homogeneous quadratic vector fields defined on the plane. The main results obtained are as follows. Main results: Let \(F\) be a homogeneous quadratic vector field defined on the plane. Then the following assertions are equivalent: (1) \(F\) is complete; (2) \(F\) is quadratic-affine or the equation \(\dot X=F(X)\) is equivalent, by a linear change of coordinates, to a system \[ \dot x=y(ax+by), \qquad \dot y=y(ex+dy), \] where \((a+d)^2- 4(ad-bc)<0\).
- University of Montpellier France
- University of Montpellier France
- Universidad Autónoma Metropolitana Mexico
completeness, Dynamics induced by flows and semiflows, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, quadratic vector fields
completeness, Dynamics induced by flows and semiflows, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, quadratic vector fields
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