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?


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