2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60886We study groups of homeomorphisms of R, each of whose elements have at most one fixed point. In particular we prove that any such group of C^2 diffeomorphisms is topologically conjugate to an affine group.references added, new theorem added :topological characterization of affine groups on RDynamical SystemsGroup Theorytext