Quasiperiodic Flows and Algebraic Number Fields
by
Lennard F. Bakker
Brigham Young University

An incomplete, but nontrivial invariant of the smooth conjugacy class of a complete flow, generated by a vector field X on a manifold P, is the multiplier group which is the set of nonzero real a such that R_*X=aX for a diffeomorphism R of P.

For each algebraic number field F of degree n over Q, a quasiperiodic flow on Tⁿ is constructed whose multiplier group is the group of units of the ring of integers in F. This construction is illustrated through examples for algebraic extensions of Q of low degree.

Date received: February 21, 2003