On the adiabatic theorem for the Hamiltonian system of differential equations in the classical mechanics, I

Abstract

Let H(p, q, s) be a Hamiltonian containing a parameter s Roughly speaking, a quantity I(p, q, s) which is a global integral of the system 1 ) dp/dt----3H/q(p, q, s), dq/dt=3H/p(p, q, s) for every fixed s (l:>sO), is called an adiabatic invariant of (1), if I(p, q, t/a) is conserved along all (nearly all)' trajectories of the following system