A STATE SPACE ISOMORPHISM THEOREM F0R MINIMAL DYNAMICAL SYSTEMS

Consider a discrete time dynamical system x_(k 1)=f(x_k) on a compact metric space M, wheref: M→M is a continuous map. Let h:M→R~k be a continuous output function. Suppose that all ofthe positive orbits of f are dense and that the system is observable. We prove that any outputtrajectory of the system determines f and h and M up to a homeomorphism.If M is a compactAbelian topological group and f is an ergodic translation, then any output trajectory determinesthe system up to a translation and a group isomorphism of the group.