2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171035In rational dynamics, we prove the existence of a polynomial that satisfies the Topological Collet-Eckmann condition, but which has a recurrent critical orbit that is not Collet-Eckmann. This shows that the converse of the main theorem in [11] does not hold. In interval dynamics, we show that the Collet-Eckmann property for recurrent critical orbits is not a topological invariant for real polynomials with negative Schwarzian derivative. This contradicts a conjecture of Swiatek [22].49 pages, 2 figuresDynamical Systems37D25 (Primary) 37E05, 37F10, 37G15, 37B10 (Secondary)text