Wouldn't the KAM theorem apply to the stable orbits? But for the chaotic orbits there was some good work a few years back by Boekholt & Portegies Zwart. They

Wouldn't the KAM theorem apply to the stable orbits? But for the chaotic orbits there was some good work a few years back by Boekholt & Portegies Zwart. They built an arbitrary-precision N-body integrator and found that the results of ordinary N-body simulations are statistically identical to arbitrary precision integrations: https://arxiv.org/abs/1411.6671 https://arxiv.org/abs/1411.6671