Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree -3
In this paper we study the polynomial integrability of natural Hamiltonian systems with two degrees of freedom having a homogeneous potential of degree k given either by a polynomial, or by an inverse of a polynomial. For k = -2, -1, . . . , 3, 4 their polynomial integrability has been characterized...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:150418 |
| Acceso en línea: | https://ddd.uab.cat/record/150418 https://dx.doi.org/urn:doi:10.1016/j.physd.2011.09.003 |
| Access Level: | acceso abierto |
| Palabra clave: | Hamiltonian system with 2-degrees of freedom Homogeneous potential of degree -3 Polynomial integrability |
| Sumario: | In this paper we study the polynomial integrability of natural Hamiltonian systems with two degrees of freedom having a homogeneous potential of degree k given either by a polynomial, or by an inverse of a polynomial. For k = -2, -1, . . . , 3, 4 their polynomial integrability has been characterized. Here we have two main results. First we characterize the polynomail integrability of those Hamiltonian systems with homogeneous potential of degree -3. Second we extend a relation between the nontrivial eigenvalues of the Hessian of the potential calculated at a Darboux point to a family of Hamiltonian systems with potentials given by an inverse of a homogeneous polynomial. This relation was known for such Hamiltonian system with homogeneous polynomial potentials. Finally we present three open problems related with the polynomial integrability of Hamiltonian systems with a rational potential. |
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