2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75144We prove that the Julia set $J(f)$ of at most finitely renormalizable unicritical polynomial $f:z\mapsto z^d+c$ with all periodic points repelling is locally connected. (For $d=2$ it was proved by Yoccoz around 1990.) It follows from a priori bounds in a modified Principle Nest of puzzle pieces. The proof of a priori bounds makes use of new analytic tools developed in math.DS/0505191 that give control of moduli of annuli under maps of high degree.LaTeX, 14 pages, 1 figureDynamical Systems37F45text