Perturbed rigidly isochronous centers and their critical periods

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

来源：Journal of Mathematical Analysis and Applications, 2017, 453(1): 366-382.

DOI：10.1016/j.jmaa.2017.03.081

• Perturbation
• Bifurcation of critical period
• Period bifurcation function
• Rigidly isochronous center

This paper investigates the bifurcation of critical periods from a cubic rigidly isochronous center under any small polynomial perturbations of degree n. It proves that for n = 3, 4 and 5, there are at most 2 and 4 critical periods induced by periodic orbits of the unperturbed cubic system respectively, and in each case this upper bound is sharp. Moreover, for any n > 5, there are at most [n-1/2] critical periods induced by periodic orbits of the unperturbed cubic system. An example is given to show that the upper bound in the case of n = 11 can be reached.

• 出版日期2017-9-1
• 单位北京航空航天大学