Scaling for a Critical Kolmogorov-Arnold-Moser Trajectory

Abstract

In problems involving two-dimensional area-preserving maps, stochastic regions are separated by continuous curves called Kolmogorov-Arnold-Moser trajectories. As the mapping is changed continuously, these regions may fuse via the disappearance of the intervening trajectories. Scaling arguments are presented to describe the behavior of the curves near their disappearance.