Strange attractors for the generalized Lozi-like family

Abstract

We generalize the Lozi-like family introduced in Misiurewicz and \v{S}timac work from 2017. The generalized Lozi-like family encompasses in particular certain Lozi-like maps, orientation preserving or reversing Lozi maps or large parameter regions of 2-dimensional border collision normal forms. We prove that it possesses a strange attractor, arising as a homoclinic class.