Vol. 67,   2   (1998) pp.   237-248
THE LAGRANGE THEOREM FOR MULTIDIMENSIONAL DIOPHANTINE APPROXIMATION
P. MEIGNEN
Abstract. 
In this paper we give a necessary and sufficient condition for $z$ in the floor of the Poincare half-space to have periodicity in the multidimensional Diophantine approximation by convergents using the Hermite algorithm. We examine in detail the structure of the corresponding sequences and give some examples