Periodic Solutions of Prescribed Energy for a Class of Hamiltonian Systems.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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Hamiltonian systems of ordinary differential equations model the motion of a discrete mechanical system when no frictional forces are present. A basic property of such systems is that energy is conserved. Therefore solutions of Hamiltonian systems lie on surfaces of fixed energy. The main result of this paper is a fairly general criterion for such a surface to possess a periodic solution.
- Numerical Mathematics