Analytic integrability of Hamiltonian systems with exceptional potentials
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 Remar...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:145299 |
| Acceso en línea: | https://ddd.uab.cat/record/145299 https://dx.doi.org/urn:doi:10.1016/j.physleta.2015.07.034 |
| Access Level: | acceso abierto |
| Palabra clave: | Exceptional potential Hamiltonian system with 2 degrees of freedom Homogeneous potentials of degree k Integrability |
| Sumario: | 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. |
|---|