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A note on the connectedness locus of the families of polynomials Pc(z)=z n - cz n-j

DOI: 10.1590/S0001-37652012000100002

Keywords: julia set, connectedness locus, hyperbolic components, principal components.

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Abstract:

let j be a positive integer. for each integer n > j we consider the connectedness locus mn of the family of polynomials pc(z) = zn - czn-j, where c is a complex parameter. we prove that limn→∞ mn = d in the hausdorff topology, where d is the unitary closed disk {c;|c|<1}.

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