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.
Darboux, M´ emoire sur les ´ equations diff´ erentielles alg´ ebriques du premier ordre et du premier degr´ e(M´ elanages), Bull
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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.