preprint-author: 
J. Kahn and M. Lyubich
preprint-title: 
A priori bounds for some infinitely renormalizable quadratics: II. Decorations
preprint-abstract: 

A decoration of the Mandelbrot set $M$ (called also a Misiurewicz limb) is a part of $M$ cut off by two external rays landing at some tip of a satellite copy of $M$ attached to the main cardioid. In this paper we consider infinitely renormalizable quadratic polynomials satisfying the decoration condition, which means that the combinatorics of the renormalization operators involved is selected from a finite family of decorations. For this class of maps we prove {\it a priori} bounds. They imply local connectivity of the corresponding Julia sets and the Mandelbrot set at the corresponding parameter values.

preprint-year: 
2006