Abstract In a prior paper, the author generalized the classical factor theorem of Sinai to actions of arbitrary countably infinite groups. In the present paper, we use this theorem and the techniques of its proof in order to study connections between positive entropy phenomena and the Koopman representation.
of the Koopman eigenfunctions. Overall, the “tuples” of Koopman eigenfunctions, eigenvalues, and modes enable us to: (a) transform state space so that the dynamics appear to be linear, (b) determine the temporal dynamics of the linear system, and (c) reconstruct the state of the original system from our new linear representation. In