Relations between ergodicity and observability

Abstract

Aspects of global observability (GO) for some standard examples of chaotic systems are considered, the underlying philosophy being that such systems should be easy to observe and should be observed by large classes of scalar functions. Consideration is given to GO for piecewise monotone maps of the interval (a standard example of a chaotic system). Attention is then given to GO for ergodic translations on compact (metrizable) topological groups; the most familiar examples are the irrational translation flows on the n-torus.