Analytic-non-integrability of an integrable analytic Hamiltonian system
| Autor: | Gaetano Zampieri, Gianluca Gorni |
|---|---|
| Rok vydání: | 2005 |
| Předmět: |
Discrete mathematics
Power series Equilibrium point Integrable system Liouville integrability Real analytic non-integrability analytically non-integrable Hamiltonians Hamiltonian system power series expansions Computational Theory and Mathematics Liouville integrable Hamiltonians Geometry and Topology Superintegrable Hamiltonian system Analysis Mathematical physics Mathematics |
| Zdroj: | Differential Geometry and its Applications. 22:287-296 |
| ISSN: | 0926-2245 |
| DOI: | 10.1016/j.difgeo.2005.01.004 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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