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Semiconjugacy of Quasiperiodic Flows and Finite Index Subgroups of Multiplier Groups

Lennard Bakker
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Abstract

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 $n$.

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Lennard Bakker. 2004-08-11. Semiconjugacy of Quasiperiodic Flows and Finite Index Subgroups of Multiplier Groups. https://arxiv.org/abs/math/0408158

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