Strange attractors for the family of orientation preserving Lozi maps

We extend the result of Michał Misiurewicz assuring the existence of strange attractors for the parametrized family {f(a,b)} of orientation reversing Lozi maps to the orientation preserving case. That is, we rigorously determine an open subset of the parameter space for which an attractor A(a,b) of f(a,b) always exists and exhibits chaotic properties. Moreover, we prove that the attractor is maximal in some open parameter region and arises as the closure of the unstable manifold of a fixed point on which f(a,b)|A(a,b) is mixing. We also show that A(a,b) vary continuously with parameter (a,b) in the Hausdorff metric.