# Contribution of individual degrees of freedom to Lyapunov vectors in many-body systems

## TL;DR

This paper introduces a diagnostic based on Lyapunov vectors to identify regions in phase space that contribute most to chaos, demonstrated on a mean field model where it highlights the separatrix vicinity.

## Contribution

It presents a novel method using the weight δI from Lyapunov vectors to characterize chaotic regions in many-body systems.

## Key findings

- The diagnostic effectively highlights the vicinity of the separatrix.
- It works even when the separatrix is barely present.
- The method provides insight into the structure of chaos in the model.

## Abstract

We use the weight $\delta$I, deduced from the estimation of Lyapunov vectors, in order to characterise regions in the kinetic (x, v) space with particles that most contribute to chaoticity. For the paradigmatic model, the cosine Hamiltonian mean field model, we show that this diagnostic highlights the vicinity of the separatrix, even when the latter hardly exists.