On the finite cyclicity of open period annuli

DOI10.1215/00127094-2010-005zbMATH Open1205.34030arXiv0807.0512OpenAlexW3101430728MaRDI QIDQ963734

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Publication date: 13 April 2010

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Abstract: 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 $X_{l}ambda$ of $X_0$ is finite, provided that $X_0$ is either Hamiltonian, or generic Darbouxian vector field.

Full work available at URL: https://arxiv.org/abs/0807.0512

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