CYCLICITY OF SEVERAL QUADRATIC REVERSIBLE SYSTEMS WITH CENTER OF GENUS ONE | Zendy

Long Chen | Zendy; Xianzhong Ma | Zendy; Gemeng Zhang | Zendy; Chengzhi Li | Zendy

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CYCLICITY OF SEVERAL QUADRATIC REVERSIBLE SYSTEMS WITH CENTER OF GENUS ONE

Author(s) -

Long Chen,

Xianzhong Ma,

Gemeng Zhang,

Chengzhi Li

Publication year - 2011

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2011030

Subject(s) - genus , quadratic equation , mathematics , center (category theory) , biology , zoology , chemistry , geometry , crystallography

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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