Integrability of Hamiltonian systems with two degrees of freedom and homogenous potential of degree zero
We provide necessary conditions in order that the Hamiltonian systems with Hamiltonian H = 1/2 (p2 1 + p2 2) + V (q1,q2), and one of the following potentials V1 = a0q1 + a1q2/a2q1 + a3q2, V2 = a0q2 1 + a1q1q2 + a2q2 2/a3q2 1 + a4q1q2 + a5q2 2, V3 = a0qn 2 + a1qn-1 2 q1 + ... + anqn 1/qn 1, are integ...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:222632 |
| Acceso en línea: | https://ddd.uab.cat/record/222632 https://dx.doi.org/urn:doi:10.4236/jamp.2018.611184 |
| Access Level: | acceso abierto |
| Palabra clave: | Darboux points Hamiltonian system Homogeneous potentials of degree zero Liouville integrability |
| Sumario: | We provide necessary conditions in order that the Hamiltonian systems with Hamiltonian H = 1/2 (p2 1 + p2 2) + V (q1,q2), and one of the following potentials V1 = a0q1 + a1q2/a2q1 + a3q2, V2 = a0q2 1 + a1q1q2 + a2q2 2/a3q2 1 + a4q1q2 + a5q2 2, V3 = a0qn 2 + a1qn-1 2 q1 + ... + anqn 1/qn 1, are integrable in the Liouville sense. |
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