2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223950We study the connection between conjugations of a special kind of dynamical systems, called P-configurations, and solutions to homogeneous Cauchy type functional equations. We find that any two regular P-configurations are conjugate by a homeomorphism, but cannot be conjugate by a diffeomorphism. This leads us to the following conclusion (resolving an open problem posed by Paneah): there exist continuous nonlinear solutions to the functional equation: f(t) = f((t+1)/2) + f((t-1)/2), t \in [-1,1] .8 pagesClassical Analysis and ODEsDynamical Systems39B22; 37B99text