Abstract
For a polynomial planar vector field of degree n ⩾ 2 with generic invariant algebraic curves we show that the maximum number of algebraic limit cycles is 1 + ( n − 1 ) ( n − 2 ) / 2 when n is even, and ( n − 1 ) ( n − 2 ) / 2 when n is odd. Furthermore, these upper bounds are reached.
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