# 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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