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.