Operator-Theoretic Identification of Closed Sub- Systems of Dynamical Systems

A central problem of dynamical systems theory is to identify a reduced description of the dynamical process one can deal easier. In this paper we present a systematic method of identifying those closed sub-systems of a given discrete time dynamical system in the frame of operator theory. It is shown that this problem is closely related to finding invariant sigma algebras of the dynamics.

Index Terms – closed sub-dynamics, sigma algebras, operator theory.