On the numerical optimization of KAM estimates by classical perturbation theory

A recently proposed algorithm for the estimate of the threshold above which a certain torus disappears, which combines classical Birkhoff normalization procedure with KAM theory, is reconsidered and improved. This is done by studying the particular case of the forced pendulum Hamiltonian {Mathematical expression}, and considering the golden torus. We find that there exists an optimal order N of normalization, and the ratio between the estimate thus obtained and the experimental value turns out to be ∼19. A possible explanation of such result is also suggested.