Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree -3
Llibre, Jaume ![Identificador ORCID](/img/uab/orcid.ico)
(Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mahdi, Adam (University of North Carolina at Charlotte. Mathematics Department)
Valls, Clàudia 1973-
![Identificador ORCID](/img/uab/orcid.ico)
(Universidade Técnica de Lisboa. Departamento de Matemática)
Fecha: |
2011 |
Resumen: |
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. |
Ayudas: |
Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
|
Nota: |
Agraïments: The third author is partially supported by FCT through CAMGDS, Lisbon. |
Derechos: |
Tots els drets reservats. ![](/img/licenses/InC.ico) |
Lengua: |
Anglès |
Documento: |
Article ; recerca ; Versió acceptada per publicar |
Materia: |
Hamiltonian system with 2-degrees of freedom ;
Homogeneous potential of degree -3 ;
Polynomial integrability |
Publicado en: |
Physica D. Nonlinear phenomena, Vol. 240 (2011) , p. 1928-1935, ISSN 0167-2789 |
DOI: 10.1016/j.physd.2011.09.003
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