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arXiv · 0807.0512

On the finite cyclicity of open period annuli

Lubomir Gavrilov·Dmitry Novikov
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Abstract

Let $Π$ 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 $Π$ under a given multi-parameter analytic deformation $X_λ$ of $X_0$ is finite, provided that $X_0$ is either Hamiltonian, or generic Darbouxian vector field.

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Lubomir Gavrilov, Dmitry Novikov. 2008-07-03. On the finite cyclicity of open period annuli. https://doi.org/10.1215/00127094-2010-005

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