Hausdorff Dimension of the Julia Set for Complex Polynomial z(z d + c)

The dynamics of complex quadratic polynomials z 2 + c has been studied extensively. In this paper we get one upper bound of the radius of the filled Julia set of fc(z )= z(z d + c), by Theorem of de Branges in univalent functions. As its application, a lower bound of the Hausdorff dimension for the Julia set of fc(z )= z(z d + c) is obtained.