Équidistribution presque partout modulo 1 de suites oscillantes perturbées – II : cas liouvillien unidimensionnel

Benoît Rittaud¹

¹ Laboratoire d'Analyse, Géométrie et Applications Institut Galilée Université Paris 13 av. J.-B. Clément 93430 Villetaneuse, France

Colloquium Mathematicum, Tome 96 (2003) no. 1, pp. 55-73.

Résumé

We extend the results on uniform distribution modulo 1 given in [3] to sequences of the form $(t(h_nF(n{\mit \Theta })+\varepsilon _nh'_n))_n$, where $(h_n)_n$, $(h'_n)_n$ and $(h_n/h'_n)_n$ are polynomially increasing sequences, $(\varepsilon _n)_n$ a bounded sequence, $F$~: ${\mathbb R}\rightarrow {\mathbb R}$ essentially a $1$-periodic $C^3$ function, ${\mit \Theta }$ and $t$ real numbers (the case $F$~: ${\mathbb R}^d\rightarrow {\mathbb R}$ and ${\mit \Theta }\in {\mathbb R}^d$ for $d>1$ will be treated in a separate article). We remove the diophantine hypothesis on ${\mit \Theta }$ needed in [3], and add a technical hypothesis on $h_n$.

Détail

DOI : 10.4064/cm96-1-6

Mots-clés : extend results uniform distribution modulo given sequences form mit theta varepsilon where n polynomially increasing sequences varepsilon bounded sequence mathbb rightarrow mathbb essentially periodic function mit theta real numbers mathbb rightarrow mathbb mit theta mathbb treated separate article remove diophantine hypothesis mit theta needed technical hypothesis