Lorentzian non-stationary dynamical systems

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