Perturbations of quadratic centers of genus one

By S. Gautier, L. Gavrilov, Iliya D. Iliev. 2007

63 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3dc82adb714ba46c41975ebed7915deea4e47581

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Jordi Villadelprat
2. Maite Grau
3. Francesc Mañosas

In Statistical and Nonlinear Physics

1. Maite Grau
2. Francesc Mañosas
3. Jordi Villadelprat

Citations in the corpus

• A Chebyshev criterion for Abelian integrals (2008, methodology): “Our last examples of application come from the paper of Gautier, Gavrilov and Iliev [8], where a program for finding the cyclicity of the period annuli of quadratic systems with centers of genus one is presented.”
• Bounding the number of zeros of certain Abelian integrals (2011, background): “[6, 7, 8]), the authors use complex analysis and algebraic topology (analytic continuation, argument principle, monodromy, PicardLefschetz formula, .”