Perturbations of quadratic centers of genus one

Details Perturbations of quadratic centers of genus one Perturbations of quadratic centers of genus one

2007-05-11

arxiv.org/abs/0705.1609v2

Discrete Contin. Dyn. Syst. 25 (2009), no. 2, 511-535

Mathematics

Dynamical Systems

28 pages

Scientific paper

We propose a program for finding the cyclicity of period annuli of quadratic systems with centers of genus one. As a first step, we classify all such systems and determine the essential one-parameter quadratic perturbations which produce the maximal number of limit cycles. We compute the associated Poincare-Pontryagin-Melnikov functions whose zeros control the number of limit cycles. To illustrate our approach, we determine the cyclicity of the annuli of two particular reversible systems.

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