Prime flows in topological dynamics

We present some results in topological dynamics and number theory. The number-theoretical results are estimates of the rates of convergence of sequences {fx26-1}, where na is irrational, a is taken mod 1, and 0<β<1. One of these results is used to construct a homorphism T of a compact metric space X such that the minimal flow (X, T) had no nontrivial homomorphic images, i.e. is a prime flow. We define an infinite family of such flows, and describe other interesting properties of these flows.