Per citar aquest document: http://ddd.uab.cat/record/150418
Scopus: 5 cites, Web of Science: 4 cites,
Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree -3
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mahdi, Adam (University of North Carolina at Charlotte. Mathematics Department)
Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)

Data: 2011
Resum: 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.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: Hamiltonian system with 2–degrees of freedom ; Homogeneous potential of degree -3 ; Polynomial integrability
Publicat a: Physica D. Nonlinear Phenomena, Vol. 240 (2011) , p. 1928-1935, ISSN 0167-2789

DOI: 10.1016/j.physd.2011.09.003


15 p, 852.9 KB

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