【摘要】WecharacterizetheLiouvillianandanalyticintegrabilityofthequadraticpolynomialvectorfieldsinR2havinganinvariantellipse.Moreprecisely,aquadraticsystemhavinganinvariantellipsecanbewrittenintotheformx=x2+y2-1+y(ax+by+c),y=x(ax+by+c),andtheellipsebecomesx2+y2=1.Weprovethat(i)thisquadraticsystemisanaly
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