Detection of Periodic Orbits in Hamiltonian Systems Using Lagrangian Descriptors

Atanasiu Stefan Demian, Stephen Wiggins

Research output: Contribution to journalArticle (Academic Journal)peer-review

14 Citations (Scopus)

Abstract

The purpose of this paper is to apply Lagrangian Descriptors, a concept used to describe phase space structure, to autonomous Hamiltonian systems with two degrees of freedom in order to detect periodic solutions. We propose a method for Hamiltonian systems with saddle-center equilibrium and apply this approach to the classical Hénon-Heiles system. The method was successful in locating the unstable Lyapunov orbits in phase space.

Original languageEnglish
Article number1750225
Number of pages9
JournalInternational Journal of Bifurcation and Chaos
Volume27
Issue number14
DOIs
Publication statusPublished - 30 Dec 2017

Keywords

  • Hamiltonian system
  • Hénon-Heiles
  • Lagrangian descriptor
  • Lyapunov orbits
  • periodic solution

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