Strange attractors for the generalized Lozi-like family

TL;DR

This paper generalizes the Lozi-like family of maps, demonstrating that it contains strange attractors as homoclinic classes, thus broadening understanding of complex dynamics in piecewise maps.

Contribution

It introduces a generalized Lozi-like family that includes various Lozi and border collision maps, proving the existence of strange attractors within this broader class.

Findings

Existence of strange attractors as homoclinic classes in the generalized family

Inclusion of orientation preserving and reversing Lozi maps

Application to large parameter regions of border collision normal forms

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.