Dynamics of functions arising from Pisot and Salem polynomials

Let Q(z) = zⁿP(z) − z^{deg P}P(z⁻¹), where P is the minimal polynomial of a Pisot number. Boyd [Duke Math. J. 44 (1977), 315–328] showed that, for (Formula presented.), Q is the product of cyclotomic polynomials and the minimal polynomial of a Salem number, say α. In this paper, we study the dynamics of the Newton map N = z − Q/Q′ induced by Q in the immediate basin U_α of α. We establish that N is a 2-fold covering map of U_α onto itself. Furthermore, there exists a conformal mapping φ of U_α onto the open unit disk D such that (Formula presented.) for all z∈D.