Details

Autor(en) / Beteiligte

• Petit, Bernard

Titel

θ-transformations, θ-shifts and limit theorems for some Riesz-Raikov sums

Ist Teil von

• Ergodic theory and dynamical systems, 1996-04, Vol.16 (2), p.335-364

Erscheinungsjahr

1996

Beschreibungen/Notizen

• Abstract By Fourier methods, it is possible to prove central limit theorems for Riesz-Raikov sums for any real θ > 1 and for a quite large class of functions f . The same problem is solved here for Hölder-continuous functions f and Pisot–Vijayaragavan numbers θ in a totally different way: it is shown that the question is equivalent to working with ergodic sums for suitable functions F on [0;l], and T denoting the θ-transformation x ↦ θx mod 1. In addition, limit theorems are proved on the θ-shifts, for any real θ 1.