On the denseness of the set of nonintegrable hamiltonians

For the set of Hamiltonian systems in a $2n$-dimensional phase space with Hamiltonians that are real analytic in a neighborhood of an equilibrium state of the system a generalization of Siegel's result is proved for $n>2$: the set of nonintegrable Hamiltonians is everywhere dense in the set of all Hamiltonians of the above form.