Geodesic
On the massiveness of the~set of nonintegrable Hamiltonians
Sbornik. Mathematics, Tome 83 (1995) no. 2, pp. 515-532

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A problem concerning Hamiltonians that are reduced via a convergent Birkhoff transformation to a normal form is considered. There is a well-known classical result of C. L. Siegel on the massiveness of the set of nonintegrable Hamiltonians in a neighborhood of an equilibrium state of a system with $n$ degrees of freedom. The main result of this paper, Theorem 3, asserts that Siegel's theorem is valid for $n>2$ under an additional assumption on the Diophantine properties of the eigenvalues of the linearized system. 
@article{SM_1995_83_2_a13,
     author = {S. I. Pidkuiko},
     title = {On the massiveness of the~set of nonintegrable {Hamiltonians}},
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S. I. Pidkuiko. On the massiveness of the~set of nonintegrable Hamiltonians. Sbornik. Mathematics, Tome 83 (1995) no. 2, pp. 515-532. http://geodesic.mathdoc.fr/item/SM_1995_83_2_a13/