A Higher-Order Period Function and Its Application

作者：Peng Linping; Lu Lianghaolong; Feng Zhaosheng^*

来源：International Journal of Bifurcation and Chaos, 2015, 25(10): 1550140.

DOI：10.1142/S0218127415501400

• Bifurcation function
• critical periods
• homogeneous perturbation
• rigidly isochronous center
• period annulus

This paper derives explicit formulas of the qth period bifurcation function for any perturbed isochronous system with a center, which improve and generalize the corresponding results in the literature. Based on these formulas to the perturbed quadratic and quintic rigidly isochronous centers, we prove that under any small homogeneous perturbations, for epsilon in any order, at most one critical period bifurcates from the periodic orbits of the unperturbed quadratic system. For e in order of 1, 2, 3, 4 and 5, at most three critical periods bifurcate from the periodic orbits of the unperturbed quintic system. Moreover, in each case, the upper bound is sharp. Finally, a family of perturbed quintic rigidly isochronous centers is shown, which has three, for epsilon in any order, as the exact upper bound of the number of critical periods.

• 出版日期2015-9
• 单位北京航空航天大学