Minoration of the complexity function associated to a translation on the torus

Nicolas Bédaride, Jean François Bertazzon

Published 2012-07-12, updated 2013-02-17Version 4

We show that the complexity function $p_k(n)$ of a piecewise translation map conjugated to a minimal translation on the torus $\TT^k = \RR^k / \ZZ^k$ is at least $kn+1$ for every integer $n$.