# $N$-body chaos, phase-space transport and relaxation in numerical simulations

## TL;DR

This paper investigates how chaos in self-gravitating systems depends on the number of particles, revealing a scale-dependent chaos measure that lies between collisional and violent relaxation times, indicating a collective chaos timescale.

## Contribution

It demonstrates that the largest Lyapunov exponent decreases with system size, uncovering a new collective timescale in N-body gravitational dynamics.

## Key findings

- Lyapunov exponent decreases as N increases
- Lyapunov time is between collisional and violent relaxation times
- Identifies a collective chaos timescale in many-body systems

## Abstract

Using direct $N$-body simulations of self-gravitating systems we study the dependence of dynamical chaos on the system size $N$. We find that the $N$-body chaos quantified in terms of the largest Lyapunov exponent $\Lambda_{\rm max}$ decreases with $N$. The values of its inverse (the so-called Lyapunov time $t_\lambda$) are found to be smaller than the two-body collisional relaxation time but larger than the typical violent relaxation time, thus suggesting the existence of another collective time scale connected to many-body chaos.