Isomorphism classes of products of powers for graphic flows

Abstract

A graphic flow is a totally minimal flow such that the only minimal subsets of the product flow are the graphs of the powers of the defining homeomorphism [2]. We consider flows of the form $(X^{k},T^{L})$, where $(X,T)$ is graphic, $k$ is a positive integer, and $L:\{1,\ldots,k\}\to {\Bbb Z}\setminus \{0\}$. It is shown that the isomorphism classes of these flows are determined by the cardinality of $L^{-1}(p)$.