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ABELIAN INTEGRALS FOR A KIND OF NON-HAMILTONIAN INTEGRABLE SYSTEMS UNDER CUBIC POLYNOMIAL PERTURBATIONS

YAN SONG

Department of Mathematics, Bohai University, Jinzhou 121000, P. R. China

https://doi.org/10.1142/S0218127411028799Cited by:0 (Source: Crossref)

Abstract

In this paper, we investigate the number of isolated zeros of the Abelian integrals for a kind of non-Hamiltonian integrable systems with one center and two invariant straight lines and with other orbits formed by quartics. It is proved that the exact upper bound of the number of isolated zeros of the Abelian integrals under cubic polynomial perturbations is equal to two.

This work was supported by the Natural Science of Foundation of China (Grant No. 61070242) and by the Science Research Project of Educational Department of Liaoning Province (JYT2008009).

Keywords:

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