时间周期哈密尔顿系统的Ergodic行为

Ergodic Behavior of the Time Periodic Hamilton System

本文拟用PDE方法,在时间1-周期Hamilton函数H(x,t,p)关于(x,t,p)连续,关于p强制条件下,证明存在c≤c∈R,使得函数u(x,t)-ct在T^n×[0,∞)有下界,u(x,t)-ct在T^n×[0,∞)有上界,其中u(x,t)是Hamilton-Jacobi方程的粘性解.

In this paper,we intend to use the PDE method to prove that there existsc≤c∈R such that u(x,t)-ct is bounded from below and u(x,t)-ct is bounded from above on T^n×[0,∞)when the time 1-periodic Hamiltonian function H(x,t,p)is continuous on(x,t,p)and coercive on p,where u(x,t)is the viscosity solution of the associated Hamilton-Jacobi equation.