On the integrability of Hamiltonian systems with d degrees of freedom and homogenous polynomial potential of degree n

Jaume Llibre, Clàudia Valls

Research output: Contribution to journalArticleResearch

Abstract

© 2018 World Scientific Publishing Company. We consider Hamiltonian systems with d degrees of freedom and a Hamiltonian of the form H = 1 2=i=1dp12 + V (q 1,...,qd), where V is a homogenous polynomial of degree n ≥ 3. We prove that such Hamiltonian systems with n odd or n = 4m, have a Darboux first integral if and only if they have a polynomial first integral.
Original languageEnglish
Article number1750045
JournalCommunications in Contemporary Mathematics
Volume20
DOIs
Publication statusPublished - 1 Dec 2018

Keywords

  • Darboux first integrals
  • Darboux polynomials
  • exponential factors
  • Hamiltonian systems
  • polynomial integrability
  • weight-homogenous differential systems

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