Home > Articles > Published articles > Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree -3 |
Date: | 2011 |
Abstract: | 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. |
Grants: | Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 |
Note: | Agraïments: The third author is partially supported by FCT through CAMGDS, Lisbon. |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Hamiltonian system with 2-degrees of freedom ; Homogeneous potential of degree -3 ; Polynomial integrability |
Published in: | Physica D. Nonlinear phenomena, Vol. 240 (2011) , p. 1928-1935, ISSN 0167-2789 |
Postprint 15 p, 852.9 KB |