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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 PoincaréPontryagin-Melnikov functions whose zeros control… (More)

Let X be a quadratic vector field with a center whose generic orbits are algebraic curves of genus one. To each X we associate an elliptic surface (a smooth complex compact surface which is a genus one fibration). We give the list of all such vector fields and determine the corresponding elliptic surfaces.

- Maggie Jarry, M Devémy, Sébastien Gautier
- Gastroenterologie clinique et biologique
- 2009

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