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

19 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	American 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

Access to Document

10.1017/S0143385708000898

Cite this

@article{e4224c71d083464c9d02b24888fadd80,

title = "Some effective results for ×a×b",

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.",

author = "Jean Bourgain and Elon Lindenstrauss and Philippe Michel and Akshay Venkatesh",

year = "2009",

month = dec,

doi = "10.1017/S0143385708000898",

language = "American English",

volume = "29",

pages = "1705--1722",

journal = "Ergodic Theory and Dynamical Systems",

issn = "0143-3857",

publisher = "Cambridge University Press",

number = "6",

}

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

M3 - Article

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 -

Some effective results for ×a×b

Abstract

Access to Document

Other files and links

Fingerprint

Cite this