Global dynamics of the integrable Armbruster-Guckenheimer-Kim galactic potential

Jaume Llibre, Claudia Valls

Research output: Contribution to journalArticleResearch

3 Citations (Scopus)


© 2019, Springer Nature B.V. We study the global dynamics of the completely integrable Armbruster-Guckenheimer-Kim galactic potential. In these cases this system has two first integrals H1 and H2 independent and in involution. Let Ih1 and Ih2 be the set of points of the phase space on which H1 and H2 take the values h1 and h2, respectively. The sets Ih1h2=Ih1∩Ih2 are invariant by the dynamics. We characterize the global flow on these sets and we describe the foliation of the phase space by the invariant sets Ih1h2.
Original languageEnglish
Article number130
JournalAstrophysics and Space Science
Publication statusPublished - 1 Aug 2019


  • Armbruster-Guckenheimer-Kim galactic potential
  • Complete integrability
  • Invariant manifolds


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