Lorentzian non-stationary dynamical systems

TL;DR

This paper introduces Lorentzian Anosov families, explores their geometric properties, and defines Lorentzian shadowing properties, contributing to the understanding of non-stationary Lorentzian dynamical systems.

Contribution

It develops the concept of Lorentzian Anosov families, proves their tangent space splitting, and introduces Lorentzian shadowing properties with related results.

Findings

Unique tangent space splitting for Lorentzian manifolds

Continuity of splitting via semi-Riemannian connection

Introduction of Lorentzian shadowing properties and initial results

Abstract

In this paper, we introduce a Lorentzian Anosov family (LAfamily) up to a sequence of distributions of null vectors. We prove for each p Mi, where Mi is a Lorentzian manifold for i Z the tangent space Mi at p has a unique splitting and this splitting varies continuously on a sequence via the distance function created by a unique torsion-free semi-Riemannian connection. We present three examples of LA-families. Also, we define Lorentzian shadowing property of type I and II and prove some results related to this property.