Closed Characteristics on Singular Energy Levels of Second-order Lagrangian Systems
نویسندگان
چکیده
We provide a lower bound on the number of closed characteristics on singular energy levels of second-order Lagrangian systems in the presence of saddle-focus equilibria. The hypotheses on the Lagrangian are mild, and the bound is given in terms of the number of saddle-foci and a potential function determined by the Lagrangian. The method of proof is variational, combining techniques to minimize near a saddle-focus and an analog of the method of broken geodesics.
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