平面非自治Hamilton方程的Lagrange稳定性

On Lagrange stability of planar non-autonomous Hamilton equation

研究了平面非自治Hamilton方程dx/dt=H/y(x,y,t),dy/dt=-H/x(x,y,t)的稳定性.其中:Hamilton函数H(x,y,t)=x2m/2m+y2n/2n+H1(x,y,t);H1是关于x和y的多项式,关于t为C∞且满足H1(x,y,t+1)=H1(x,y,t).证明了当H1关于x和y的次数满足一定条件时,该平面非自治Hamilton方程具有Lagrange稳定性.

The planar non-autonomous Hamilton equation dx/dt=δH/δy（x,y,t）,dy/dt=-δH/δx（x,y,t） was discussed with the Hamilton function H（x,y,t）=x^2m/2m＋y^2n/2n＋H1（x,y,t）,where H1 was a polynomial function of x and y and in C^∞ for t and Ha （x,y,t ＋ 1 } =H1 （x,y,t）. It was proved that when the multiples ofx and y of H1 satisfied a gived condition, the planar non-autonomous Hamilton equations would be Lagrange stable.