Geodesic
On the denseness of the set of nonintegrable hamiltonians
Izvestiya. Mathematics , Tome 41 (1993) no. 1, pp. 143-155

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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. 
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     title = {On the denseness of the set of nonintegrable hamiltonians},
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S. I. Pidkuiko. On the denseness of the set of nonintegrable hamiltonians. Izvestiya. Mathematics , Tome 41 (1993) no. 1, pp. 143-155. http://geodesic.mathdoc.fr/item/IM2_1993_41_1_a6/