First integrals and Darboux polynomials of natural polynomial Hamiltonian systems

Isaac A. García, Maite Grau, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

6 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 languageEnglish
Pages (from-to)4746-4748
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume374
Issue number47
DOIs
Publication statusPublished - 25 Oct 2010

Keywords

  • Darboux polynomial
  • Hamiltonian system
  • Polynomial first integral
  • Polynomial potential

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