The Chaotic Saddle in the Lozi map, autonomous and non-autonomous versions

Abstract

In this paper we prove the existence of a chaotic saddle for a piecewise linear map of the plane, referred to as the Lozi map. We study the Lozi map in its orientation and area preserving version. First, we consider the autonomous version of the Lozi map to which we apply the Conley-Moser conditions to obtain the proof of a chaotic saddle. Then we generalize the Lozi map on a non-autonomous version and we prove that the first and the third Conley-Moser conditions are satisfied, which imply the existence of a chaotic saddle. Finally, we numerically demonstrate how the structure of this nonautonomous chaotic saddle varies as parameters are varied.