The coexistence of quasi-periodic and blow-up solutions in a class of Hamiltonian systems

The coexistence of quasi-periodic solutions and blow-up phenomena in a class of higher dimensional Duffing-type equations is proved in this paper. Moreover, we show that the initial point sets for both kinds of solutions are of infinite Lebesgue measure in the phase space. For the part of quasi-periodic solutions, the tool we used is the small twist theorem for higher dimensional cases.