5 problems

Transcendentality–multiplier group conjecture. A quasiperiodic flow $\psi$ is transcendental if and only if

Algebraicity–multiplier group conjecture. A quasiperiodic flow $\psi$ is $F$-algebraic if and only if $M_\psi$ is a finite index subgroup of ${\mathfrak o}_F^*$.

Let $\phi$ be a quasiperiodic flow on $T^n$ generated by a constant vector field $X$. Call $\phi$ algebraic if it is $F$-algebraic for a real algebraic number field $F$ of degree…

Let $F$ be a real algebraic number field of degree $n$ over $\mathbb{Q}$, and let $T^n$ denote the $n$-torus. The multiplier-group equality conjecture. There exists a quasiperiodic…

Let $T^n$ be the $n$-torus, let $\phi$ be a quasiperiodic flow on $T^n$ generated by a constant vector field $X$, and let $F$ be a real algebraic number field of degree $n$ over…