A covering cocycle which does not grow linearly

Abstract

A cocycle h : X × Z m → R n h:X \times {Z^m} \to {R^n} of a Z m {Z^m} action on a compact metric space, provides an R n {R^n} suspension flow (analogous to a flow under a function) on a space X h {X_h} which may not be Hausdorff or even T 1 {T_1} . Linear growth of h h guarantees that X h {X_h} is a Hausdorff space; when m = n m = n , linear growth is a consequence of X h {X_h} being Hausdorff and a covering condition. This paper contains the construction of a cocycle h : X × Z → R 2 h:X \times Z \to {R^2} which does not grow linearly yet produces a locally compact Hausdorff space with the covering condition. The Z Z action used in the construction is a substitution minimal set.