Inverses, Powers and Cartesian products of topologically deterministic maps

TL;DR

This paper investigates the properties of topologically deterministic dynamical systems, showing that inverse and product systems may lose determinism, but powers of the map retain determinism if the product system is deterministic.

Contribution

It demonstrates the conditions under which inverse, powers, and Cartesian products of topologically deterministic maps preserve determinism.

Findings

Inverse and product systems may not be deterministic.

If the product system is deterministic, then all positive powers are deterministic.

Determinism is not necessarily preserved under inverse and product operations.

Abstract

We show that if (X,T) is a topological dynamical system with is deterministic in the sense of Kamiski, Siemaszko and Szymaski then T^{-1} and the product system need not be determinstic in this sense. However if the product system is deterministic then T^n is deterministic for all integers n>0.