Iterated Monodromy Group of Rational Maps
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We describe the iterated monodromy groups of rational functions of the form ∫c(z) = 1+c/z² , where the parameter c lies in certain components of the parameter plane which are attached to the main cardioid. Such a group is determined uniquely by a rational angle determined by the parameter. We give a proof for iterated monodromy groups of such parameters and then give iterated monodromy groups of parameters lying in finer limbs by a so-called tuning method.
Chao, Qian (2018). Iterated Monodromy Group of Rational Maps. Master's thesis, Texas A & M University. Available electronically from