The Multiplier Group of a Quasiperiodic Flow

Abstract

As an absolute invariant of smooth conjugacy, the multiplier group described the types of space-time symmetries that the flow has, and for a quasiperiodic flow on the $n$-torus, is the determining factor of the structure of its generalized symmetry group. It is conjectured that a quasiperiodic flow is F-algebraic if and only if its multiplier group is a finite index subgroup of the group of units in the ring of integers of a real algebraic number field F, and that a quasiperiodic flow is transcendental if and only if its multiplier group is {1,-1}. These two conjectures are partially validated for n greater or equal to 2, and fully validated for n=2.