🚀 go-pugleaf

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.