A priori bounds for some infinitely renormalizable quadratics: III. Molecules
Abstract
In this paper we prove a priori bounds for infinitely renormalizable quadratic polynomials satisfying a ``molecule condition''. Roughly speaking, this condition ensures that the renormalization combinatorics stay away from the satellite types. These a priori bounds imply local connectivity of the corresponding Julia sets and the Mandelbrot set at the corresponding parameter values.
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