一类非多项式型周期Hamilton系统的Lagrange稳定性

The Lagrangian Stability on a Class of Non-Polynomial Periodic Hamiltonian Systems

证明了非多项式型周期Hamilton方程dx/dt= H/ y（x,y,t）,dy/dt=- H/ x（x,y,t）的Lagrange稳定性，其中Hamilton函数H（x，y，t）=x^2m/2m＋y^2n/2n＋∑i,j∈I^x^iy^jpi,j（x,y,t）,pi,j是x,y和t的C^∞周期函数，i，j满足适当的上限条件．

In this paper, we prove the Lagrangian stability for the following nonpolynomialtype periodic Hamiltonian system： dx/dt= H/ y（x,y,t）,dy/dt=- H/ x（x,y,t） with the Hamiltonian H（x,y,t）= x^2m/2m＋y^2n/2n＋H1（x,y,t）, where H1 is C^∞ and periodic on x, y and t, i,j in I satisfy some suitable inequalities.