2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152779We study scaling function geometry. We show the existence of the scaling function of a geometrically finite one-dimensional mapping. This scaling function is discontinuous. We prove that the scaling function and the asymmetries at the critical points of a geometrically finite one-dimensional mapping form a complete set of $C^{1}$-invariants within a topological conjugacy class.Dynamical Systemstext