On the Darboux integrability of the logarithmic galactic potentials
We study the logarithmic Hamiltonians H=(p +p )∕2+log(1+x+y∕q), which appear in the study of the galactic dynamics. We characterize all the invariant algebraic hypersurfaces and all exponential factors of the Hamiltonian system with Hamiltonian H. We prove that this Hamiltonian system is completely...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:221289 |
| Acceso en línea: | https://ddd.uab.cat/record/221289 https://dx.doi.org/urn:doi:10.1016/j.geomphys.2017.07.019 |
| Access Level: | acceso abierto |
| Palabra clave: | Logarithmic galactic potential Polynomial integrability Rational integrability Darboux polynomials Darboux first integrals Invariant algebraic hypersurfaces |
| Sumario: | We study the logarithmic Hamiltonians H=(p +p )∕2+log(1+x+y∕q), which appear in the study of the galactic dynamics. We characterize all the invariant algebraic hypersurfaces and all exponential factors of the Hamiltonian system with Hamiltonian H. We prove that this Hamiltonian system is completely integrable with Darboux first integrals if and only if q=±1. |
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