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Mosc. Math. J., 2009, Volume 9, Number 4, Pages 855–866 (Mi mmj367)  

Projective limit cycles

Hossein Movasati, Evilson Vieira

Instituto de Matemática Pura e Aplicada, IMPA, Rio de Janeiro, Brazil

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.

DOI: https://doi.org/10.17323/1609-4514-2009-9-4-855-866

Full text: http://www.ams.org/.../abst9-4-2009.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 34C07
Received: June 16, 2008
Language:

Citation: Hossein Movasati, Evilson Vieira, “Projective limit cycles”, Mosc. Math. J., 9:4 (2009), 855–866

Citation in format AMSBIB
\Bibitem{MovVie09}
\by Hossein~Movasati, Evilson~Vieira
\paper Projective limit cycles
\jour Mosc. Math.~J.
\yr 2009
\vol 9
\issue 4
\pages 855--866
\mathnet{http://mi.mathnet.ru/mmj367}
\crossref{https://doi.org/10.17323/1609-4514-2009-9-4-855-866}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2663993}
\zmath{https://zbmath.org/?q=an:1187.37071}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000273089600006}


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