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

作者：Song Yan^*

来源：International Journal of Bifurcation and Chaos, 2011, 21(3): 789-798.

DOI：10.1142/S0218127411028799

• Non-Hamiltonian integrable system
• Picard-Fuchs equation
• cubic polynomial perturbations
• Abelian integral

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.

• 出版日期2011-3
• 单位渤海大学