Abstract
Let an unperturbed multidimensional polynomial vector field have an invariant plane L and let the system restricted to this plane be Hamiltonian with a quadratic Hamilton function. Now take a polynomial perturbation of this system. The new system has an invariant surface close to L and the system restricted to it has a certain number of limit cycles. We strive to estimate this number. The linearization of this problem leads to estimation of the number of zeros of certain integral, which is a generalization of the abelian integral. We estimate this number of zeros by C 1+C 2 n, where n is the degree of the perturbation.
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Leszczyński, P., Żoładek, H. Limit Cycles Appearing After Perturbation of Certain Multidimensional Vector Fields. Journal of Dynamics and Differential Equations 13, 689–709 (2001). https://doi.org/10.1023/A:1012858008962
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DOI: https://doi.org/10.1023/A:1012858008962