Quasiperiodic flows and algebraic number fields

We classify a quasiperiodic flow as either algebraic or transcendental. For an algebraic cluasiperiodic flow phi on the n-torus, T-n, we prove that an absolute invariant of the smooth conjugacy class of phi, known as the multiplier group, is a subgroup of the group of units of the ring of integers,in a real algebraic number field F of degree a 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 T-n 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 cluasiperiodic flows from the transcendental ones.