Time-independent canonical perturbation theory for nearly multiple-periodic systems

Abstract

A modification of the classical canonical time-independent perturbation theory is presented for nearly multiple-periodic systems having Hamiltonians of the form H=H0(Jalpha )+ lambda H1(walpha ,Jalpha ;qk,pk)+ lambda 2H2(walpha ,Jalpha ;qk,pk)+... where H1,H2,... are periodic functions of the angles walpha . The perturbation procedure is based on averaging of the Hamilton-Jacobi equation over the angles walpha . The existence of constants of motion to all orders of the perturbation theory for both non-degenerate and intrinsically degenerate systems is shown.