This note, like the previous one [1], is mainly based on the fact that a geodesic flow on a closed Riemannian manifold of negative curvature satisfies certain conditions (U) formulated below. Therefore it seems appropriate to consider arbitrary dynamical systems satisfying these conditions. A dynamical system is understood throughout this paper to be defined on an m-dimensional connected closed smooth manifold Wm, to be of class C2 and to have an integral invariant.* The dynamical system may have either continuous or discrete time. Since a dynamical system with continuous time is often called a flow, I shall call a system with discrete time a cascade. A flow is determined by giving a vector field f(w) of class C2 on Wm; Tt w, where t runs through all real numbers, denotes the solution of the system of differential equations d(Ttw)dt=f(Ttw),T0w=w.