Dynamics, integrability and topology for some classes of Kolmogorov Hamiltonian systems in R<inf>+</inf><sup>4</sup>

Jaume Llibre, Dongmei Xiao

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

© 2016 Elsevier Inc. In this paper we first give the sufficient and necessary conditions in order that two classes of polynomial Kolmogorov systems in R+4 are Hamiltonian systems. Then we study the integrability of these Hamiltonian systems in the Liouville sense. Finally, we investigate the global dynamics of the completely integrable Lotka–Volterra Hamiltonian systems in R+4. As an application of the invariant subsets of these systems, we obtain topological classifications of the 3-submanifolds in R+4 defined by the hypersurfaces axy+bzw+cx2y+dxy2+ez2w+fzw2=h, where a,b,c,d,e,f,w and h are real constants.
Original languageEnglish
Pages (from-to)2231-2253
JournalJournal of Differential Equations
Volume262
Issue number3
DOIs
Publication statusPublished - 5 Feb 2017

Keywords

  • Global dynamics
  • Hamiltonian system
  • Hypersurfaces
  • Liouvillian integrability
  • Topological classification

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