On the bifurcation properties of a class of differentiate mappings

The bifurcation properties of a class of differential mappings are examined. This class describes perturbed systems that are characterized in the steady-state by an invariant set of points in the period-1 region. It was found that bifurcation points of the perturbed and associated unperturbed system satisfy a strict ordering for the period-1 case. In this paper it is proven that in general there exists period-n intervals whose bifurcation points, together with the bifurcation points of the period-n points of the unperturbed system, obey the same ordering result.