Anosov structures on Margulis spacetimes (Q2013901)

A Margulis spacetime \( M\) is a quotient manifold of the three-dimensional affine space by a free, non-abelian discrete group acting as affine transformations with discrete linear part. The author studies the stable and unstable laminations of the space \(UM\) of non-wandering geodesics in \( M\) under the geodesic flow. It is shown that the stable lamination contracts under the forward flow and the unstable lamination contracts under the backward flow. More precisely, the following result is true: Theorem. There exist laminations \( L _+\) and \( L_-\) of the metric space \( UM\) such that the geodesic flow on the space of non-wandering geodesics in \(M\) contracts \(L_+\) exponentially in the forward direction of the flow and contracts \(L_-\) exponentially in the backward direction of the flow. Extending the notion of Anosov structure, the author defines the notion of Anosov representation and shows that monodromies of Margulis spacetimes are ``Anosov representations in non semi-simple Lie groups''.