Almost sure equidistribution in expansive families
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.
scientific article; zbMATH DE number 5691184