Free oscillations of prescribed energy at a saddle-point of the potential in Hamiltonian dynamics

Helmut Hofer, John F. Toland

Research output: Contribution to journalArticle


We consider a class of Hamiltonians of the form <p,p>+V(q), where the potential is even and has (a possibly highly degenerate) critical point which is a saddle at 0∈ℝ n and V(0)=0. Under certain natural conditions on V we show that the corresponding Hamiltonian system has non-trivial periodic orbits of all positive energies passing through 0. The methods employed give an illustration of the significance of monotone trajectories in the study of certain classical Hamiltonian systems.
Original languageEnglish
Pages (from-to)238-249
JournalDelft Progress Report
Publication statusPublished - 1 Jan 1985

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