visitante ::
identificación
|
|||||||||||||||
Buscar | Enviar | Ayuda | Servicio de Bibliotecas | Sobre el DDD | Català English Español |
Página principal > Artículos > Artículos publicados > Analytic integrability of Hamiltonian systems with exceptional potentials |
Fecha: | 2015 |
Resumen: | We study the existence of analytic first integrals of the complex Hamiltonian systems of the form H = 1 2 ∑ 2 i=1 p 2 i + Vl(q1, q2) with the homogeneous polynomial potential Vl(q1, q2) = α(q2 − iq1) L (q2 + iq1) k−l , l = 0, . . . , k, α ∈ C \ {0} of degree k called exceptional potentials. In Remark 2. 1 of J. Math. Phys. 46 (2005), 062901, the authors state: The exceptional potentials V0, V1, Vk−1, Vk and Vk/2 when k is even are integrable with a second polynomial first integral. However nothing is known about the integrability of the remaining exceptional potentials. Here we prove that the exceptional potentials with k even diferent from V0, V1, Vk−1, Vk and Vk/2, have no independent analytic first integral different from the Hamiltonian one. Additionally in the cases V2 and Vk−2 with k either even or odd we show that they do not have rational first integrals independent of the Hamiltonian. |
Ayudas: | Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999 |
Nota: | Agraïments: UNAB13-4E-1604. The second author is partially supported by FCT/Portugal through UID/MAT/04459/2013. |
Derechos: | Tots els drets reservats. |
Lengua: | Anglès |
Documento: | Article ; recerca ; Versió acceptada per publicar |
Materia: | Exceptional potential ; Hamiltonian system with 2 degrees of freedom ; Homogeneous potentials of degree k ; Integrability |
Publicado en: | Physics Letters. A, Vol. 379 (2015) , p. 2295-2299, ISSN 0375-9601 |
Postprint 9 p, 770.9 KB |