Let (X, f) be a topological dynamical system. We say that it is partially periodic point free up to period n, if f does not have periodic points of periods smaller than n + 1. When X is a compact connected surface, a connected compact graph, or S ∨ S ∨ · · · ∨ S, we give conditions on X, so that there exist partially periodic point free maps up to period n. We also introduce the notion of a Lef...

For a dynamical system described by a set of autonomous ordinary differential equations, an attractor can be a point, a periodic cycle, or even a strange attractor. Recently, a new chaotic system with only one stable equilibrium was described, which locally converges to the stable equilibrium but is globally chaotic. This paper further shows that for certain parameters, besides the point attrac...