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.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/694617
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 5
social impact