Some effective results for ×a×b

Jean Bourgain; Elon Lindenstrauss; Philippe Michel; Akshay Venkatesh

doi:10.1017/S0143385708000898

Some effective results for ×a×b

Jean Bourgain^*
, Elon Lindenstrauss
, Philippe Michel
, Akshay Venkatesh

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

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	English
Pages (from-to)	1705-1722
Number of pages	18
Journal	Ergodic Theory and Dynamical Systems
Volume	29
Issue number	6
DOIs	https://doi.org/10.1017/S0143385708000898
State	Published - Dec 2009

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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.

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Some effective results for ×a×b

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