We introduce the polynomial Hamiltonian H(q(1), q(2), p(1), p(2)) := (q(2)(2) + (q(1)(2) + q(2)(2))(2))p(1) -q(1)q(2)p(2) 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. © 2005 Elsevier B.V. All rights reserved.

Analytic-non-integrability of an integrable analytic Hamiltonian system

GORNI, Gianluca;
2005

Abstract

We introduce the polynomial Hamiltonian H(q(1), q(2), p(1), p(2)) := (q(2)(2) + (q(1)(2) + q(2)(2))(2))p(1) -q(1)q(2)p(2) 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. © 2005 Elsevier B.V. All rights reserved.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11390/694617
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