This question is motivated by the finitness of limit cycles for polynomial vector fields on $\mathbb{R}^2$
Assume that $X,Y$ are two independent polynomial vector fields on $\mathbb{R}^{3}$ such that the distribuation $\{X,Y\}$ is an integrable distribution. So we have a foliation.
Is it true to say that there are only a finite number of compact leaves(torus) with nontrivial holonomy?
What is an example of this situation such that the foliation has at least one compact leaf?
