Geodesic
On the Distribution of nθ Modulo 1
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1020-1024

Voir la notice de l'article provenant de la source Cambridge University Press

In recent work of E. Arthurs and L. A. Shepp on a problem of H. Dym concerning the existence of an ergodic stationary stochastic process with zero entropy (cf. 1), the function dθ(n) was introduced as follows:For an irrational number θ, let be the sequence of points {lθ}, 1 ≦ l ≦ n, (where {x} denotes x — [x], the fractional part of x) and define* dθ (n) = max(ai — a i-1), 1 ≦ in + 1. 
Graham, R. L.; Lint, J. H. Van. On the Distribution of nθ Modulo 1. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1020-1024. doi: 10.4153/CJM-1968-099-1
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