| Volume 1, Number 4, 2011, Pages 439-447 DOI：10.11948/2011030 |
| Cyclicity of several quadratic reversible systems with center of genus one |
| Long Chen,Xianzhong Ma,Gemeng Zhang,Chengzhi Li |
| Keywords:Cyclicity of period annulus |
| Abstract: |
| By using the Chebyshev criterion to study the number of zeros of Abelian integrals, developed by M. Grau, F. Ma\(\~n\)osas and J. Villadelprat in [2], we prove that the cyclicity of period annulus of the quadratic reversible systems with center of genus one, classified as (r8), (r13) and (r16) by S. Gautier, L. Gavrilov and I. D. Iliev in [1], under quadratic perturbations is two. These results partially give a positive answer to the conjecture 1 in [1]. |
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