Abstract
We consider the family of rational maps given by where with the variable and the parameter . It is known [1] that when there are small copies of the Mandelbrot set symmetrically located around the origin in the parameter plane. These baby Mandelbrot sets have ‘antennas’ attached to the boundaries of Sierpiński holes. Sierpiński holes are open simply connected subsets of the parameter space for which the Julia sets of are Sierpiński curves. In this paper we generalize the symmetry properties of and the existence of the baby Mandelbrot sets to the case when where n is not necessarily equal to d.
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