On the geometry in the neighborhood of infinity of quadratic differential systems with a weak focus
Copyright policy )On the geometry in the neighborhood of infinity of quadratic differential systems with a weak focus
The authors study the phase portraits near infinity of quadratic vector fields which have a finite critical point that is a weak focus. The global phase portrait of these quadratic vector fields in the whole Poincaré sphere, but just when the weak focus has order three, has been already studied by \textit{J. C. Artés} and \textit{J. Llibre} in Publ. Mat. 41, 7--39 (1997; Zbl 0880.34031). Apart from the study of the weak focus of order smaller than three, the novelty introduced in the reviewed paper is that the different phase portraits are characterized in terms of intersection multiplicities and divisors associated to some complex projective curves obtained from the differential equation. One advantage of this approach is that all these objects have a geometrical meaning and are affine invariant.
weak focus, Dynamics induced by flows and semiflows, Singularities of vector fields, topological aspects, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, multiplicity, phase portrait, divisor, quadratic system, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
weak focus, Dynamics induced by flows and semiflows, Singularities of vector fields, topological aspects, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, multiplicity, phase portrait, divisor, quadratic system, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
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