CYCLICITY OF SEVERAL QUADRATIC REVERSIBLE SYSTEMS WITH CENTER OF GENUS ONE

Long Chen; Xianzhong Ma; Gemeng Zhang; Chengzhi Li

doi:10.11948/2011030

2011 Volume 1 Issue 4

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Long Chen, Xianzhong Ma, Gemeng Zhang, Chengzhi Li. CYCLICITY OF SEVERAL QUADRATIC REVERSIBLE SYSTEMS WITH CENTER OF GENUS ONE[J]. Journal of Applied Analysis & Computation, 2011, 1(4): 439-447. doi: 10.11948/2011030

Citation:

Long Chen, Xianzhong Ma, Gemeng Zhang, Chengzhi Li. CYCLICITY OF SEVERAL QUADRATIC REVERSIBLE SYSTEMS WITH CENTER OF GENUS ONE[J]. Journal of Applied Analysis & Computation, 2011, 1(4): 439-447. doi: 10.11948/2011030

CYCLICITY OF SEVERAL QUADRATIC REVERSIBLE SYSTEMS WITH CENTER OF GENUS ONE

1 Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, China;
2 School of Mathematical Sciences, Peking University, Beijing 100871, China

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Abstract

Abstract

By using the Chebyshev criterion to study the number of zeros of Abelian integrals, developed by M. Grau, F. Mañosas 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].
- Cyclicity of period annulus /
- Quadratic reversible center of genus one /
- Abelian integrals /
- Chebyshev property
MSC: 34C07;34C08;37G15

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References

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