Open AccessSolutions of a Lagrangian system on 𝕋 2
Author(s) -
Paul H. Rabinowitz
Publication year - 1999
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.96.11.6037
Subject(s) - homoclinic orbit , lagrangian , homotopy , chaotic , mathematics , mathematical physics , type (biology) , physics , mathematical analysis , pure mathematics , bifurcation , quantum mechanics , computer science , nonlinear system , biology , artificial intelligence , ecology
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 ofH± and variational arguments that, in fact, there is a much richer structure of homoclinics and heteroclinics tov± . Indeed, the system admits chaotic solutions.