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...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Valls, Clàudia|||0000-0001-8279-1229
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
Descripción
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.