A priori bounds for some infinitely renormalizable quadratics: III. Molecules

Details A priori bounds for some infinitely renormalizable quadratics: III. Molecules A priori bounds for some infinitely renormalizable quadratics: III. Molecules

2007-12-14

arxiv.org/abs/0712.2444v1

Mathematics

Dynamical Systems

Scientific paper

In this paper we prove {\it 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 {\it a priori bounds} imply local connectivity of the corresponding Julia sets and the Mandelbrot set at the corresponding parameter values.

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