title: A note on the connectedness locus of the families of polynomials P(c)(z)=z(n) - cz(n-j).
abstract: Let j be a positive integer. For each integer n > j we consider the connectedness locus M(n) of the family of polynomials P(c)(z)=z(n) - cz(n-j), where c is a complex parameter. We prove that lim n→∞ M(n) = D in the Hausdorff topology, where D is the unitary closed disk {c;|c|≤1}.
authors.affiliation: Departamento de Matemática, ICEX, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brasil. dcam@mat.ufmg.br
authors.forename: Carlos
authors.initials: C
authors.lastname: Arteaga
authors.forename: Alexandre
authors.initials: A
authors.lastname: Alves