【摘要】 对于哈密顿函数为一定正的齐二次多项式与一高次齐次多项式之和的情况,本文讨论了对应的系统在原点周围周期轨道族周期的单调性。主要结果是:当高次项是奇数次齐次多项式时,周期函数是单调增加的;当高次项是四次齐次多项式时,得到了单调的充要条件。更多还原

【Abstract】 In this paper,the monotonicity of the period function for the family of periodic trajectories surrounding the origin in a class of Hamiltonian system with Hamiltonian H (x,y)is studied,where H(x,y)is thesum of a positive definite homogeneous polynomial of degree two and a homogeneous poly- nomial of higher degree. The main results are.the period function is increasing when the higher degree is odd;the necessary and sufficient conditions for the monotonicity of the period function are obtained when the higher degree is four.更多还原