AN EXAMPLE OF A UNIVERSALLY OBSERVABLE FLOW ON THE TORUS

In this paper we examine the question of existence of a two-dimensiona l universally observable system, i.e., dynamics which are observable b y every continuous nonconstant real-valued function on the state space . We are motivated by the work of D. McMahon, who proved that a class of three-dimensional manifolds with horocycle flow have this property. We examine this example and are able to give sufficient conditions fo r a flow to be universally observable. We then use these conditions to show the existence of a continuous universally observable flow on the torus. The proofs involve techniques and concepts from topological dy namics and dynamical systems on the torus.