Lorentzian non-stationary dynamical systems

Abstract

In this paper, we introduce a Lorentzian Anosov family (LA-family) up to a sequence of distributions of null vectors. We prove for each p ∈ M_i, where M_i is a Lorentzian manifold for i ∈ ℤ the tangent space M_i 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.

Subject Classification:

• 37D05
• 37D20
• 53B30
• 37C50

Keywords:

• Lorentzian Anosov family
• Semi-Riemannian connection
• Lorentzian solenoid
• Lorentzian shadowing property of type I and II