Application of Greene's method and the MacKay residue criterion to the double pendulum

The double pendulum is a non-integrable Hamiltonian system which exhibits the scenario of transition to global chaos via the decay of a golden mean KAM torus. We apply Greene's method and the MacKay residue criterion and compute the threshold to global chaos. We find that MacKay's method is superior to Greene's since it requires much less numerical work but nevertheless gives accurate results.