Electronic Journal of Differential Equations, Vol. 2008(2008),
No. 82, pp. 1-37. Title: When singular points determine
quadratic systems Authors: Joan C. Artes (Univ. Autonoma de
Barcelona, Catalonia, Spain) Jaume Llibre (Univ. Autonoma de
Barcelona, Catalonia, Spain) Nicolae Vulpe (Academy of Science
of Moldova, Moldova) Abstract: When one considers a quadratic
differential system, one realizes that it depends on 12
parameters of which one can be fixed by means of a time change.
One also can notice that fixing 4 finite real singular points
plus 3 infinite real ones (all its possible singular points)
implies to fix 11 conditions, that is, 11 equations that the
parameters must satisfy. Since these conditions are linear with
respect to the parameters, it is obvious to think that the
system will be determined, except that the fixed conditions are
incompatible with a quadratic differential system having
finitely many singular points. In this paper we prove exactly
this. That is, if we fix the position of the 7 si