Connectivity of Julia Sets for Singularly Perturbed Rational Maps
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چکیده
In this paper we consider the family of rational maps of the form F λ (z) = z n + λ/z n where n ≥ 2. It is known that there are two cases where the Julia sets of these maps are not connected. If the critical values of F λ lie in the basin of ∞, then the Julia set is a Cantor set. And if the critical values lie in the preimage of the basin surrounding the pole at 0, then the Julia set is a Cantor set of concentric simple closed curves around the origin. We prove in this paper that, in all other cases, the Julia set of F λ is a connected set.
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تاریخ انتشار 2012