  We classify a quasiperiodic flow as either algebraic or transcendental. For
an algebraic quasiperiodic flow on the n-torus, we prove that an absolute
invariant of the smooth conjugacy class of this flow, known as the multiplier
group, is a subgroup of the group of units of the ring of integers in a real
algebraic number field of degree n over Q. We also prove that for any real
algebraic number field F of degree n over Q, there exists an algebraic
quasiperiodic flow on the n-torus whose multiplier group is exactly the group
of units of the ring of integers in F. We support and formulate the conjecture
that the multiplier group distinguishes the algebraic quasiperiodic flows from
the transcendental ones.
