Displaying similar documents to “Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian Systems with convex Hamiltonians.”

Periodic solutions for second order Hamiltonian systems on an arbitrary energy surface

Chengfu Che, Xiaoping Xue (2012)

Annales Polonici Mathematici

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Two theorems about the existence of periodic solutions with prescribed energy for second order Hamiltonian systems are obtained. One gives existence for almost all energies under very natural conditions. The other yields existence for all energies under a further condition.