Almost sure equidistribution in expansive families
type: Item
instance of: scholarly article
title: Almost sure equidistribution in expansive families
zbMATH Open document ID: 1189.11040
DOI: 10.1016/S0019-3577(09)00017-2
author: Michael Björklund
author: Daniel Schnellmann
published in: Indagationes Mathematicae. New Series
publication date: 2010-04-08T00:00:00Z
review text: Equidistribution of sequences of real numbers modulo \(1\) is a very classical and well-studied area of research. For example, Koksma proved that for almost every \(\theta>1\), the sequence \(\theta^j \bmod 1, j\geq 1\), is equidistributed in the unit circle \(\mathbb{T}\), i.e. for any interval \(A\) of \(\mathbb{T}\), \[ \frac{\#\{j: \theta^j\bmod 1 \in A, 1\leq j\leq N\}}{N} \longrightarrow |A|, \quad\text{as}\quad N\longrightarrow\infty. \] The paper under review discusses a geometric method to generalize Koksma's result based on the techniques developed by Benedicks and Carleson in one-dimensional dynamics.
Mathematics Subject Classification ID: 11K38
Mathematics Subject Classification ID: 11K36
zbMATH DE Number: 5691184
zbMATH Keywords: equidistribution
zbMATH Keywords: geometric method
zbMATH Keywords: expansion
zbMATH Keywords: distortion
MaRDI profile type: Publication
cites work: On iterations of \(1-\alpha x^2\) on \((-1,1)\)
cites work: Sequences, discrepancies and applications
cites work: Q3710597
cites work: Q4761189
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full work available at URL: s0019-3577(09)00017-2
OpenAlex ID: W2106857876
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description: scientific article; zbMATH DE number 5691184