On the relationship between Lozi maps and max-type difference equations

TL;DR

This paper explores the connection between generalized Lozi maps and max-type difference equations through topological conjugation, analyzing their dynamics and providing numerical simulations and open problems.

Contribution

It establishes a topological conjugation linking Lozi maps with max-equations and investigates the dynamics of specific families, offering new insights into their relationship.

Findings

Relationship between Lozi maps and max-equations established

Numerical simulations illustrate the dynamics

Open problems proposed for future research

Abstract

In the present work we revise a transformation that links generalized Lozi maps with max-type difference equations. In this view, according to the technique of topological conjugation, we relate the dynamics of a concrete Lozi map with a complete uniparametric family of max-equations, and we apply this fact to investigate the dynamics of two particular families. Moreover, we present some numerical simulations related to the topic and, finally, we propose some open problems that look into the relationship established between generalized Lozi maps and max-equations.