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Four limit cycles from perturbing quadratic integrable systems by quadratic polynomials

In this paper, we give a positive answer to the open question: Can there exist 4 limit cycles in quadratic near-integrable polynomial systems? It is shown that when a quadratic integrable system has two centers and is perturbed by quadratic polynomials, it can generate at least 4 limit cycles with (3,1) distribution. The method of Melnikov function is used.

preprint2010arXivOpen access
Pei YuMaoan Han
math.DS
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Pei YuMaoan Han

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