Accessible Mandelbrot Sets in the Family zn + λ/zn
2016
In this paper we prove the existence of infinitely many accessible Mandelbrot
sets in the parameter plane for the family of maps zn + λ/zn when n > 1.
These are Mandelbrot sets for which the cusp of the main cardioid touches the outer
boundary of the connectedness locus. We show that there is a unique such Mandelbrot
set at the landing point of each external ray that is periodic under θ → nθ.
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