【摘要】 本文讨论奇点不对称的一类平面三次Hamilton扰动系统,研究该系统与奇点具对称性系统的分支的不同性质。给出了判定函数的计算方法,并证明了下图所示的三种极限环分布可以实现。更多还原

【Abstract】 In this paper the two-parameter family of disturbed Hamiltonian system of the form dx/d=y, dy/dt=x+2∝x²-x³-μy（q（x, y）-λ） （1）is discussed where q（x, y）=a₁₁x²+2a₁₂xy+a₂₂y²+2a₁₃x+2a₂₃y. The existence of a two parameter family of periodic orbits depending on λ, μ and an one-parameter family of homoclinic or beteroclninc orbits depending on μ is studied by detection curves to obtain qualitative behaviour of （1）. The presence of local and global bifurcatiens of（1）is detected and two distributions of limit cycles which can not appear in quadratic systems could be found（see Figl） The results in this paper are concerned with Hilbert’s 16 th problem.更多还原