• DOI:10.2307/1971148
• Corpus ID: 56409744

On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface

@article{Ekeland1980OnTN,
  title={On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface},
  author={Ivar Ekeland and J. M. Lasry},
  journal={Annals of Mathematics},
  year={1980},
  volume={112},
  pages={283}
}

• I. Ekeland, J. Lasry
• Published 1 September 1980
• Mathematics
• Annals of Mathematics

kbstract In this paper, we look for periodic solutions, with prescribed energy h C R, of Hamilton's equations: (H) a H (x, p), p aH (x, p). ap Ax It is assumed that the Hamiltonian H is convex on R" x R", and that the origin (0, 0) is an isolated equilibrium. It is also assumed that some ball B around the origin can be found such that the energy surface H'(h) lies outside B but inside v'2 B. Under these assumptions, we prove that there are at least n distinct periodic orbits of the Hamiltonian flow (H) with energy level h.