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

2007/12/14 by Jeremy Kahn, Kahn, Jeremy, Mikhail Lyubich +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.0712.2444

arxiv created 2007/12/14 · arxiv updated 2009/12/01

Abstract

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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