Semiconjugacy of Quasiperiodic Flows and Finite Index Subgroups of Multiplier Groups

Details Semiconjugacy of Quasiperiodic Flows and Finite Index Subgroups of Multiplier Groups Semiconjugacy of Quasiperiodic Flows and Finite Index Subgroups of Multiplier Groups

2004-08-11

arxiv.org/abs/math/0408158v1

Mathematics

Dynamical Systems

Submitted to the Proceedings of the AIMS' Fifth International Conference on Dynamical Systems and Differential Equations

Scientific paper

It will be shown that if $\phi$ is a quasiperiodic flow on the $n$-torus that is algebraic, if $\psi$ is a flow on the $n$-torus that is smoothly conjugate to a flow generated by a constant vector field, and if $\phi$ is smoothly semiconjugate to $\psi$, then $\psi$ is a quasiperiodic flow that is algebraic, and the multiplier group of $\psi$ is a finite index subgroup of the multiplier group of $\phi$. 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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