Corrigendum to “On the number of limit cycles surrounding a unique singular point for polynomial differential systems of arbitrary degree” [Nonlinear Anal. 69 (12) (2008) 4461–4469

Abstract

In the paper [B. García, J. Llibre, J.S. Pérez del Río, On the number of limit cycles surrounding a unique singular point for polynomial differential systems of arbitrary degree, Nonlinear Analysis 69 (12) (2008) 4461–4469] we studied the number of limit cycles that bifurcate from the periodic orbits of the center x ̇ = − y R ( x , y ) , y ̇ = x R ( x , y ) where R is a convenient polynomial of degree 2, when we perturb it inside the class of all polynomial differential systems of degree n . Actually, the number obtained is not correct and we can now prove that its true value is 2 [ ( n − 1 ) / 2 ] + 1 instead of ( [ ( n − 1 ) / 2 ] + 4 ) ( [ ( n − 1 ) / 2 ] + 1 ) / 2 − 1 .