Perturbation of Homoclinics and Subharmonics in Duffing's Equation.

摘要

For (lambda, mu) and (g,f) small, the equation x - x + 2x cubed + g(x) = - lambda x + mu(cos t + f(t))is considered near the separatrix S of the unperturbed equation (lambda, mu) = (0,0). For (g,f) in a neighborhood of the zero functions, a complete description is given of the bifurcation curves in (lambda, mu) - space to homoclinic points. The perturbation of subharmonics outside S is also considered in a symmetric and nonsymmetric case.