Question about the KAM theorem

[xdrgnh]

I have an Hamiltonian with a non linear perturbation attached to it. When the perturbation parameter equals .2 the system at a certain initial condition exhibits chaotic motion. I found this out graphically. I would like to calculate how large my perturbation parameter has to be analytically for the system to exhibit chaos. Would I use the KAM theorem for such a calculation? Any help will be much appreciated.

 

[Haborix]

There is the overlap criterion developed by Chirikov: link.

The general procedure is to go to the action-angle coordinates of the integrable system, and then having written the perturbation in terms of these variables expand it in Fourier series.