# Criterion for Stability of a Special Relativistically Covariant Dynamical System

## TL;DR

This paper investigates the stability of a relativistic Duffing oscillator using a geometric method, identifying conditions for chaos and extending classical stability analysis into relativistic regimes.

## Contribution

It introduces a relativistic generalization of the geometric method to analyze the stability of a relativistic Duffing oscillator, a novel approach in this context.

## Key findings

- Identified a threshold for external force leading to chaos.
- Validated the relativistic analysis with Poincaré plots.
- Extended classical stability concepts to relativistic systems.

## Abstract

We study classically the problem of two relativistic particles with an invariant Duffing-like potential which reduces to the usual Duffing form in the nonrelativistic limit. We use a special relativistic generalization (RGEM) of the geometric method (GEM) developed for the analysis of nonrelativistic Hamiltonian systems to study the local stability of a relativistic Duffing oscillator. Poincar'e plots of the simulated motion are consistent with the RGEM. We found a threshold for the external driving force required for chaotic behavior in the Minkowski spacetime.