Periodic solutions with prescribed minimal period for convex autonomous hamiltonian systems

@article{Ekeland1985PeriodicSW,
  title={Periodic solutions with prescribed minimal period for convex autonomous hamiltonian systems},
  author={Ivar Ekeland and Helmut H. Hofer},
  journal={Inventiones mathematicae},
  year={1985},
  volume={81},
  pages={155-188}
}
Clarke has shown that the problem of findingT-periodic solutions for a convex Hamiltonian system is equivalent to the problem of finding critical points to a certain functional, dual to the classical action functional. In this paper, we relate the Morse index of the critical point to the minimal period of the correspondingT-periodic solution. In particular, we show that if the critical point is obtained by the Ambrosetti-Rabinowitz mountain-pass theorem the corresponding solution has minimal… 
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