2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106236Let $K$ be a number field and $ϕ\in K(z)$ a rational function. Let $S$ be the set of all archimedean places of $K$ and all non-archimedean places associated to the prime ideals of bad reduction for $ϕ$. We prove an upper bound for length of finite orbits of $ϕ$ in $\mathbb{P}_1(K)$ depending only on the cardinality of $S$.13 pages. Changed contentNumber TheoryDynamical Systems11G99 (Primary) 14E05 (Secondary)text