p-adic foliation and equidistribution

We show that if μ is a measure on ℝ/ℤ ergodic under the x m map with positive entropy, then μ-a.s. {a_nx} is equidistributed, for a significantly larger collection of integer sequences a_n than was previously known. In particular, we show that μ-a.s. {rⁿx} is equidistributed as long as m does not divide any power of r (this was previously known only if r and m are relatively prime). The proof uses the p-adic analogue of results from the theory of smooth dynamical systems.