Semiconjugacy of Quasiperiodic Flows and Finite Index Subgroups of Multiplier Groups
نویسنده
چکیده
It will be shown that if φ is a quasiperiodic flow on the n-torus that is algebraic, if ψ is a flow on the n-torus that is smoothly conjugate to a flow generated by a constant vector field, and if φ is smoothly semiconjugate to ψ, then ψ is a quasiperiodic flow that is algebraic, and the multiplier group of ψ is a finite index subgroup of the multiplier group of φ. 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.
منابع مشابه
The Multiplier Group of a Quasiperiodic Flow
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 unit...
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