%0 Journal Article
%T Equidistribution in the $d$-dimensional $a$-adic solenoids
%A Roman Urban
%J Uniform Distribution Theory
%D 2011
%I Mathematical Institute of the Slovak Academy of Sciences
%X Given a probability measure $mu$ on the $d$-dimensional $a$-adic solenoid $\Omega_a^d$ and an endomorphism $T$ of $\Omega_a^d,$ we consider the relation between uniform distribution of the sequence $T^n\mathbf{x}$ for $\mu$-almost all $\mathbf{x}\in\Omega_a^d$ and the behavior of $\mu$ relative to the translations by some rational subgroups of $\Omega_a^d.$ The main result of this note is an extension of the corresponding result for the $d$-dimensional torus $\mathbb T^d$ due to B. Host \cite{H}.
%K Uniform distribution modulo 1
%K equidistribution in probability
%K a-adic solenoid
%K topological dynamics
%U http://www.boku.ac.at/MATH/udt/vol06/no1/3Urban11-1.pdf