Critical perturbation in standard map: A better approximation

Abstract

Direct computation of the transition time between neighbor resonances in the standard map, as a function of the perturbation parameter $K$, allows for improving the accuracy of the critical perturbation value up to $K_{cr}-K_g < 2.5\times 10^{-4}$ that is by a factor of about 50 as compared to the previous result due to MacKay and Percival.