goedde@shape.mps.ohio-state.edu (Christopher G. Goedde) (03/01/91)
Hello all, I am looking for pointers to references about using the Melnikov function for calculating the width of a separatrix layer in a Hamiltonian system with a periodic perturbation. The unperturbed system has a homoclinic orbit--it is the width of the chaotic layer around this orbit that I am trying to calculate. The references I have consulted so far are Guckenheimer & Holmes and Lichtenberg & Lieberman. Using their prescriptions, I have calculated the (alleged) width of the layer. Unfortunately, the calculation disagrees with my numerical simulations of the system with regard to the scaling of the layer's width with epsilon (the perturbation strength). My Melnikov calculation indicates that the width should be proportional to epsilon, while numerics show that the width is actually proportional to sqrt(epsilon). The above references deal primarily with looking for the zeros of the Melnikov function, and not with the ins and outs of using it to calculate the layer's width. So my question is, are there some references/experts out there who could enlighten me on this? Thanks, Chris Goedde goedde@shape.mps.ohio-state.edu Mail or post as deemed appropriate.