Invariant Tori of Impulsive Duffing-Type Equations via KAM Technique

Abstract

A method via the KAM technique is introduced to study the existence of invariant tori and quasiperiodic solutions for impulsive Duffing-type equations with time period 1. Basing on several planar symplectic homeomorphisms and some estimates of impulsive perturbations under each symplectic homeomorphisms, we prove via the Moser's twist theorem the boundedness (Lagrange stability) and the existence of an invariant circle for the equation with area-preserving impulsive terms. And this invariant circle having any rotation number $\omega>\omega_0$ with some $\omega_0>0$, so we obtain also that the solutions starting from the circle are quasiperiodic with frequencies $\omega$ and 1.