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;
2005-01-01
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.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
nonAnalyticScaricato.pdf
non disponibili
Tipologia:
Altro materiale allegato
Licenza:
Non pubblico
Dimensione
292.06 kB
Formato
Adobe PDF
|
292.06 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
