First integrals and Darboux polynomials of natural polynomial Hamiltonian systems

Isaac A. García; Maite Grau; Jaume Llibre

doi:10.1016/j.physleta.2010.09.060

First integrals and Darboux polynomials of natural polynomial Hamiltonian systems

Isaac A. García, Maite Grau, Jaume Llibre

Department of Mathematics

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8 Citations (Scopus)

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. © 2010 Elsevier B.V.

Original language	English
Pages (from-to)	4746-4748
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	374
Issue number	47
DOIs	https://doi.org/10.1016/j.physleta.2010.09.060
Publication status	Published - 25 Oct 2010

Keywords

Darboux polynomial
Hamiltonian system
Polynomial first integral
Polynomial potential

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10.1016/j.physleta.2010.09.060

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AU - Grau, Maite

AU - Llibre, Jaume

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N2 - 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. © 2010 Elsevier B.V.

AB - 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. © 2010 Elsevier B.V.

KW - Darboux polynomial

KW - Hamiltonian system

KW - Polynomial first integral

KW - Polynomial potential

U2 - 10.1016/j.physleta.2010.09.060

DO - 10.1016/j.physleta.2010.09.060

M3 - Article

VL - 374

SP - 4746

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ER -

First integrals and Darboux polynomials of natural polynomial Hamiltonian systems

Abstract

Keywords

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