  The paper establishes the property of splittability of billiard boundary
sequences in n dimensional cube into subsequences of fractional parts. This
reveals a new property of integrable and weak perturbated Hamilton systems:
under a simple assumption, the boundary motion of elliptic orbits on stable KAM
tori, if considering in cartesian coordinates, can be splitted into a countable
set of discrete rotations. The rate of the split process, expressed in terms of
some exceptional sets density, in dependence of number-theoretical
characteristics of the orbits frequencies, is also examined.
