Infinite Order Linear Collision Duffing Equation Invariant Torus

Impact oscillator is an important model of non-smooth dynamical systems. There are also many relationship with lots of application problems, such as Fermi-Ulam accer-ator, dual billiards, celestial mechanics and so on. Dynamics of impact oscillator needs to be further mathematical research, although many numerical results are known.In this paper, we deal with the existence of invariant tori for suplinear impact oscillators where x' denotes and 1-periodic, i.e, p(t+1)=p(t) for any t∈R.At first, we transform the impact Duffing-type equation to a Hamiltonian system with impact; then set a series of transformations in Hamiltonian system, by using implicit function theorem; finally, apply Moser's twist theorem, we get the existence of invariant tori for impact Duffing-type equation in extended phase-space, we also prove that there exist infinitely many quasiperiodic solutions, and every solution of impact Duffing-type equation can not go to infinity or go to zero if the initial value is sufficiently large.