**Edit:  [This  is  a  real  coefficient  version  of the  current post.](https://mathoverflow.net/questions/327721/a-complex-limit-cycle-not-intersecting-the-real-plane2?noredirect=1&lq=1)**

Is there a polynomial vector  field $X$ with complex coefficients  on $\mathbb{C}^2$ with the property quoted bellow?

>There is  a  regular leaf $L$ whose holonomy, along at least one closed curve on it,  is not trivial but $L$  does not intersect the real part $im (z)=im(w)=0,\;(z,w) \in \mathbb{C}^2$.


# Note:

 A leaf with non trivial holonomy is called a complex limit cycle, according to the terminology used in the  video lecture by Ilyashenko described in the following answer:

https://mathoverflow.net/questions/171988/the-error-in-petrovski-and-landis-proof-of-the-16th-hilbert-problem/173609#173609