Generic Existence of Invariant Cantori in Pendulum-Type Equations*

In this paper we prove that generically for QsQ t, x.gC` T2.there exists a dense set VsV Q. of irrational numbers in R such that the pendulum-type equation ¨xsQx t, x.possesses an invariant cantorus with rotation number 1, v. for every v gV.