Global Existence of Homoclinic and Periodic Orbits for a Class of Autonomous Hamiltonian Systems

B. Buffoni, J. F. Toland

Research output: Contribution to journalArticle

Abstract

When nonlinear, reversible fourth order Hamiltonian systems have a saddle-focus at a hyperbolic equilibrium of zero energy, geometric conditions on the Hamiltonian are given to ensure the existence of a symmetric homoclinic orbit which is the limit of certain specific zero-energy periodic orbits uniformly on compact time intervals. When the equilibrium is a centre. the existence of a large amplitude, zero-energy, periodic orbit which is not given by Lyapunov’s Centre Theorem is proved.

Original languageEnglish
Pages (from-to)104-120
Number of pages17
JournalJournal of Differential Equations
Volume118
Issue number1
DOIs
Publication statusPublished - 1 May 1995

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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