# 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} }

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…

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