Lyapunov spectrum of a relativistic stochastic flow in the Poincar\'e group

TL;DR

This paper analyzes the Lyapunov spectrum and stable manifolds of stochastic flows on the Poincaré group related to relativistic processes, providing insights into their stability and dynamical behavior.

Contribution

It introduces the computation of Lyapunov spectra for relativistic stochastic flows on the Poincaré group, a novel application in stochastic differential geometry.

Findings

Lyapunov spectrum characterized for the flows

Stable manifolds identified for the processes

Insights into stability of relativistic stochastic flows

Abstract

We determine the Lyapunov spectrum and stable manifolds of some stochastic flows on the Poincar\'e group associated to Dudley's relativistic processes.