First integrals and Darboux polynomials of natural polynomial Hamiltonian systems |
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| Authors: | Isaac A García Maite Grau |
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| Institution: | a Departament de Matemàtica, Universitat de Lleida, Avda. Jaume II, 69, 25001 Lleida, Catalonia, Spain
b Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain |
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| Abstract: | In this Letter we study some aspects of the relationship between the existence of Darboux polynomials and additional polynomial first integrals in natural polynomial Hamiltonian systems with a finite number of degrees of freedom. More precisely, first we improve results of the paper of Maciejewski and Przybylska A.J. Maciejewski, M. Przybylska, Phys. Lett. A 326 (2004) 219]; and after we answer two open questions presented in that paper. |
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| Keywords: | Darboux polynomial Hamiltonian system Polynomial potential Polynomial first integral |
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