On the finite cyclicity of open period annuli

Details On the finite cyclicity of open period annuli On the finite cyclicity of open period annuli

2008-07-03

arxiv.org/abs/0807.0512v1

Duke Math. J. 152 (2010), no. 1, 1-26

Mathematics

Dynamical Systems

22 pages, 1 figure

Scientific paper

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 multi-parameter analytic
deformation $X_\lambda$ of $X_0$ is finite, provided that $X_0$ is either
Hamiltonian, or generic Darbouxian vector field.

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