Critical perturbation in standard map: A better approximation

TL;DR

This paper improves the accuracy of estimating the critical perturbation value in the standard map by directly computing transition times between resonances, achieving a fiftyfold increase in precision over previous methods.

Contribution

It introduces a direct computation method for transition times that significantly refines the critical perturbation estimate in the standard map.

Findings

Critical perturbation value estimated with high precision

Achieved about 50 times better accuracy than previous results

Enhanced understanding of resonance transition dynamics

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.