Structure of Group Invariants of a Quasiperiodic Flow

Abstract

The multiplier representation of the generalized symmetry group of a quasiperiodic flow on the n-torus defines, for each subgroup of the multiplier group of the flow, a group invariant of the smooth conjugacy class of that flow. This group invariant is the internal semidirect product of a subgroup isomorphic to the n-torus by a subgroup isomorphic to that subgroup of the multiplier group. Each subgroup of the multiplier group is a multiplicative group of algebraic integers of degree at most n, which group is isomorphic to an abelian group of n by n unimodular matrices.