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.
Yablonskii, Limit cycles of a certain differential equations , Differential Equa- tions 2 (1966), 335–344 (in Russian)
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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.