Quadratic Cremona maps transform known quadratic systems with algebraic limit cycles into a new family with a degree-5 limit cycle and recover all known higher-degree families.
Evdokimenco , Behavior of integral curves of a dynamic system , Differential Equations 9 (1974), 1095–1103
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Quadratic Planar Differential Systems with Algebraic Limit Cycles via Quadratic Plane Cremona Maps
Quadratic Cremona maps transform known quadratic systems with algebraic limit cycles into a new family with a degree-5 limit cycle and recover all known higher-degree families.