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Analytic-non-integrability of an integrable analytic Hamiltonian system |
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| Authors: | Gianluca Gorni Gaetano Zampieri |
| Affiliation: | a Università di Udine, Dipartimento di Matematica e Informatica, via delle Scienze 208, I-33100 Udine UD, Italy b Università di Torino, Dipartimento di Matematica, via Carlo Alberto 10, I-10123 Torino TO, Italy |
| Abstract: | We introduce the polynomial Hamiltonian  and we prove that the associated Hamiltonian system is Liouville-C∞-integrable, but fails to be real-analytically integrable in any neighbourhood of an equilibrium point. The proof only uses power series expansions, and is elementary. |
| Keywords: | 37J35 37J30 |
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