Abstract:
In this article we study projective cycles in $\mathbb P^2_\mathbb R$. Our inspiring example is the Jouanolou foliation of odd degree which has a hyperbolic projective limit cycle. We prove that only odd degree foliations may have projective cycles and that foliations with exactly one real simple singularity have a projective cycle. We also prove that after a perturbation of a generic Hamiltonian foliation with a projective cycle, we have a projective limit cycle if and only if the perturbation is not Hamiltonian.
Key words and phrases:holomorphic foliations, holonomy, vanishing cycle.
Fulltext:
www.ams.org/.../abst9-4-2009.html 
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