A polynomial-exponential variation of Furstenberg's theorem

M. Abramoff; D. Berend

doi:10.1017/etds.2018.132

A polynomial-exponential variation of Furstenberg's theorem

M. Abramoff, D. Berend

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

1 Scopus citations

Abstract

Furstenberg's theorem asserts that the double sequence is dense modulo one for every irrational. The same holds with and replaced by any two multiplicatively independent integers. Here we obtain the same result for the sequences for any non-negative integer and irrational, and for the sequence, where is any polynomial with at least one irrational coefficient. Similarly to Furstenberg's theorem, both results are obtained by considering appropriate dynamical systems.

Original language	English
Pages (from-to)	1729-1737
Number of pages	9
Journal	Ergodic Theory and Dynamical Systems
Volume	40
Issue number	7
DOIs	https://doi.org/10.1017/etds.2018.132
State	Published - 1 Jul 2020

Keywords

Density modulo 1
Furstenberg's diophantine theorem
topological dynamics

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1017/etds.2018.132

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title = "A polynomial-exponential variation of Furstenberg's theorem",

abstract = "Furstenberg's theorem asserts that the double sequence is dense modulo one for every irrational. The same holds with and replaced by any two multiplicatively independent integers. Here we obtain the same result for the sequences for any non-negative integer and irrational, and for the sequence, where is any polynomial with at least one irrational coefficient. Similarly to Furstenberg's theorem, both results are obtained by considering appropriate dynamical systems.",

keywords = "Density modulo 1, Furstenberg's diophantine theorem, topological dynamics",

author = "M. Abramoff and D. Berend",

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N2 - Furstenberg's theorem asserts that the double sequence is dense modulo one for every irrational. The same holds with and replaced by any two multiplicatively independent integers. Here we obtain the same result for the sequences for any non-negative integer and irrational, and for the sequence, where is any polynomial with at least one irrational coefficient. Similarly to Furstenberg's theorem, both results are obtained by considering appropriate dynamical systems.

AB - Furstenberg's theorem asserts that the double sequence is dense modulo one for every irrational. The same holds with and replaced by any two multiplicatively independent integers. Here we obtain the same result for the sequences for any non-negative integer and irrational, and for the sequence, where is any polynomial with at least one irrational coefficient. Similarly to Furstenberg's theorem, both results are obtained by considering appropriate dynamical systems.

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A polynomial-exponential variation of Furstenberg's theorem

Abstract

Keywords

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