2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75957In this paper we will refine Sacksteder's theorem for groups of orientation-preserving homeomorphisms of the circle in the case that there exists a finite orbit set. We will give a categorization of the topological possibilities for the orbits of points of the circle, along with examples.30 pages, 5 figures, submitted to Topology and Its ApplicationsDynamical Systems37B05text