Solutions of a Lagrangian system on 2.

Rabinowitz, P H · Proc Natl Acad Sci U S A · 1999

basic_science · Level V

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Abstract

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.