Adding machine factorizations and iterations of quadratic polynomials

We will describe a class of factorizations of the binary adding machines, which are in a one-to-one correspondence with external rays to the Mandelbrot set. We show that, in the case of rational angles, groups generated by the factors coincide if and only if the rays land on the same point. We show how internal addresses are encoded in the structure of the corresponding iterated monodromy groups. This is a joint work with L.Bartholdi and D.Dudko.

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