RELATIONS BETWEEN ERGODICITY AND OBSERVABILITY.

The problems of controllability and observability for nonlinear systems have received a great deal of attention in the control theory literature. Most results have been for systems that have very smooth dynamics. Other results have depended heavily on C infinity properties of the underlying manifold and dynamics. The philosophy adopted here is in some sense the opposite. Questions of global observability are considered for some standard examples of systems that are 'chaotic'. The underlying philosophy is that such systems should be easy to observe and should be observed by large classes of scalar functions. Global observability for piecewise monotone maps of the interval, a standard example of a chaotic system, is discussed. Global observability for ergodic translations on compact (metrizable) topological groups, a standard class of examples of ergodic systems, is also considered.