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It will be shown that ifis a quasiperiodic flow on the n-torus that is algebraic, if is a flow on the n-torus that is smoothly conjugate to a flow generated by a constant vector field, and ifis smoothly semiconjugate to , then is a quasiperiodic flow that is algebraic, and the multiplier group of is a finite index subgroup of the multiplier group of . This will partially establish a conjecture that asserts that a quasiperiodic flow on the n-torus is algebraic if and only if its multiplier group is a finite index subgroup of the group of units of the ring of integers in a real algebraic number field of degree n.

Semiconjugacy of quasiperiodic flows and finite index subgroups of multiplier groups