Solutions of a Lagrangian system on 2.
A Lagrangian system on 2 that has been studied earlier under a geometrical condition and found to possess a pair of solutions, H+/-, homoclinic to periodic solutions, v+/-, of a given homotopy type, is considered further. It is shown with the aid of H+/- and variational arguments that, in fact, there is a much richer structure of homoclinics and heteroclinics to v+/-. Indeed, the system admits chaotic solutions.
Rabinowitz
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Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA.