Periodic Solutions for the Generalized Anisotropic Lennard-Jones Hamiltonian

Jaume Llibre, Yiming Long

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

© 2015, Springer Basel. We characterize the circular periodic solutions of the generalized Lennard-Jones Hamiltonian system with two particles in Rn, and we analyze what of these periodic solutions can be continued to periodic solutions of the anisotropic generalized Lennard-Jones Hamiltonian system. We also characterize the periods of antiperiodic solutions of the generalized Lennard-Jones Hamiltonian system on R2n, and prove the existences of (Formula Presented.) such that this system possesses no τ/2-antiperiodic solution for all (Formula Presented.), at least one τ/2-antiperiodic solution when (Formula Presented.), precisely 2n families of τ/2-antiperiodic circular solutions when (Formula Presented.), and precisely 2n+1 families of τ/2-antiperiodic circular solutions when (Formula Presented.). Each of these circular solution families is of dimension n - 1 module the S1-action.
Original languageEnglish
Pages (from-to)291-311
JournalQualitative Theory of Dynamical Systems
Volume14
Issue number2
DOIs
Publication statusPublished - 1 Oct 2015

Keywords

  • Anisotropic Lennard-Jones potential
  • Circular periodic solutions
  • Lennard-Jones potential

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