2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71777We give examples of infinitely renormalizable quadratic polynomials $F_c: z\maps to z^2+c$ with stationary combinatorics whose Julia sets have Hausdorff dimension arbitrar y close to 1. The combinatorics of the renormalization involved is close to the Chebyshev one . The argument is based upon a new tool, a ``Recursive Quadratic Estimate'' for the Poincaré series of an infinitely re normalizable map.13 pagesDynamical SystemsComplex Variables37F25; 37F45text