TY - JOUR
T1 - Some effective results for ×a×b
AU - Bourgain, Jean
AU - Lindenstrauss, Elon
AU - Michel, Philippe
AU - Venkatesh, Akshay
PY - 2009/12
Y1 - 2009/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=74349099547&partnerID=8YFLogxK
U2 - 10.1017/S0143385708000898
DO - 10.1017/S0143385708000898
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AN - SCOPUS:74349099547
SN - 0143-3857
VL - 29
SP - 1705
EP - 1722
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 6
ER -