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Subdiffusive behavior generated by irrational rotations

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Huveneers, François [UCL]

We study asymptotic distributions of the sums y(n)(x) = Sigma(n-1)(k=0) psi(x + k alpha) with respect to the Lebesgue measure, where alpha is an element of R - Q and where psi is the 1-periodic function of bounded variation such that psi(x) = 1 if x is an element of [0, 1/2[ and psi(x) = -1 if x is an element of [1 /2, 1[. For every alpha is an element of R - Q, we find a sequence (n(j))(j) subset of N such that y(nj)/root j is asymptotically normally distributed. For n >= 1, let z(n) is an element of (y(m))(m <= n) be such that parallel to z(n)parallel to(L2) = max(m <= n) parallel to y(m)parallel to(L2). If a is of constant type, we show that z(n)/parallel to z(n)parallel to(L2) is also asymptotically normally distributed. We give a heuristic link with the theory of expanding maps of the interval.

Document type Article de périodique (Journal article) – Article de recherche
Publication date 2009
Language Anglais
Journal information "Ergodic Theory and Dynamical Systems" - Vol. 29, p. 1217-1233 (2009)
Peer reviewed yes
Publisher Cambridge Univ Press (New York)
issn 0143-3857
e-issn 1469-4417
Publication status Publié
Affiliation UCL - SC/PHYS - Département de physique
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Bibliographic reference Huveneers, François. Subdiffusive behavior generated by irrational rotations. In: Ergodic Theory and Dynamical Systems, Vol. 29, p. 1217-1233 (2009)
Permanent URL http://hdl.handle.net/2078.1/35431