Abstract
ABSTRACTLet n and k be positive integers. For , we consider the connectedness locus of the family of polynomials , where c is a complex parameter. We show that the geometric limit of the connectedness locus sets , when n tends to infinity, exists and is the closed unit disk. In addition, we give an upper bound for the geometric size of .When parameter c belongs to the open unit disk, we show that the geometric limit of the Julia sets , when n tends to infinity, exists and is the unit circle. Finally, we have established some properties on the hyperbolic components of this family.
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