2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115248By means of a nested sequence of some critical pieces constructed by Kozlovski, Shen, and van Strien, and by using a covering lemma recently proved by Kahn and Lyubich, we prove that the Julia set of a polynomial is a Cantor set if and only if each component of the filled-in Julia set containing critical points is aperiodic. This result was a conjecture raised by Branner and Hubbard in 1992.29 pages, 15 figuresDynamical Systems37F10; 37F20text