On the finite cyclicity of open period annuli

Gavrilov, Lubomir; Novikov, Dmitry

Duke Math. J., Tome 151 (2010) no. 1, p. 1-26 / Harvested from Project Euclid

Résumé

Let $\Pi$ be an open, relatively compact period annulus of real analytic vector field $X_0$ on an analytic surface. We prove that the maximal number of limit cycles which bifurcate from $\Pi$ under a given multiparameter analytic deformation $X_\lambda$ of $X_0$ is finite provided that $X_0$ is either a Hamiltonian or generic Darbouxian vector field

Publié le : 2010-03-15
Classification: 34C07, 34C10

@article{1268317522,
     author = {Gavrilov, Lubomir and Novikov, Dmitry},
     title = {On the finite cyclicity of open period annuli},
     journal = {Duke Math. J.},
     volume = {151},
     number = {1},
     year = {2010},
     pages = { 1-26},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1268317522}
}

Gavrilov, Lubomir; Novikov, Dmitry. On the finite cyclicity of open period annuli. Duke Math. J., Tome 151 (2010) no. 1, pp.  1-26. http://gdmltest.u-ga.fr/item/1268317522/