Abstract
We provide effective versions of theorems of Furstenberg and RudolphJohnson regarding closed subsets and probability measures of ℝ/ℤ invariant under the action of a non-lacunary multiplicative semigroup of integers. In particular, we give an explicit rate at which the sequence {anb kx}n,k becomes dense for a,b fixed multiplicatively independent integers and x∈ℝ/ℤ Diophantine generic.
Original language | American English |
---|---|
Pages (from-to) | 1705-1722 |
Number of pages | 18 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 29 |
Issue number | 6 |
DOIs | |
State | Published - Dec 2009 |