On invariant tori of vector field under weaker non-degeneracy condition

Abstract

In this paper we prove the persistence of invariant tori for analytic perturbation of constant vector field under weaker non-degeneracy condition. In the proof we introduce a parameter q and make the steps of KAM iteration infinitely small in the speed of function \({q^{n} \epsilon}\), \({0 < q < 1}\), rather than super exponential function.