Invariant tori and Lagrange stability of pendulum-type equations (Q914932)

This paper is motivated by a question put by Moser in 1973 concerning the Lagrange stability of non-autonomous pendulum-like equations of the form \(x'=y\), \(y'=-G_ x(t,x)+p(t)\) where G and p have period 1. It is shown that such a smooth system is Lagrangian stable iff p has mean zero. It has an infinite number of invariant tori if p has mean zero, and none otherwise.