ISOMORPHISM-CLASSES OF PRODUCTS OF POWERS FOR GRAPHIC FLOWS

A graphic flow is a totally minimal flow such that the only minimal su bsets 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,..., k} --> Z\{0}. It is shown that the isomorphism classes of these flows are determine d by the cardinality of L-1(p). These results are part of an on-going analysis of joinings in measurable settings [6, 8, 10] and topological settings [2, 7, 10]. The main result is a new topological analogue of a theorem of Rudolph [12, Theorem 3.1]. A. del Junco [7, Theorem 3.4] has also obtained a topological version of Rudolph's theorem for a la rger class of maps on X-k but using a weaker notion of isomorphism.