Non-isochronicity of the center in polynomial Hamiltonian systems

作者：Wang Zhaoxia; Chen Xingwu; Zhang Weinian^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2010, 73(1): 228-243.

DOI：10.1016/j.na.2010.03.016

• Hamiltonian system
• Center
• Isochronicity
• Period coefficient
• Basis of ideal

In 2002 Jarque and Villadelprat proved that planar polynomial Hamiltonian systems of degree 4 have no isochronous centers and raised an open question for general planar polynomial Hamiltonian systems of even degree. Recently, it was proved that a planar polynomial Hamiltonian system is non-isochronous if a quantity, denoted by M(2m-2), can be computed such that M(2m-2) <= 0. As a corollary of this criterion, the open question was answered for those systems with only even degree nonlinearities. In this paper we consider the case of M(2m-2) > 0 and give a new criterion for non-isochronicity. Applying the new criterion, we also answer the open question for some cases in which some terms of odd degree are included.

• 出版日期2010-7-1
• 单位四川大学