2017/06/27 by Lu Chen, Jianhua Shen, Chen, Lu +1
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Nonlinear Waves and Solitons #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.48550/arxiv.1706.08660
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 ω>ω0 with some ω0>0, so we obtain also that the solutions starting from the circle are quasiperiodic with frequencies ω and 1.