Lozi-like maps

TL;DR

This paper introduces Lozi-like maps, a broad class of piecewise smooth plane homeomorphisms with hyperbolic attractors, and provides numerical evidence of their diverse kneading sequences compared to traditional Lozi maps.

Contribution

The paper defines Lozi-like maps and demonstrates their complex kneading sequences, extending the understanding of piecewise smooth dynamical systems.

Findings

Existence of Lozi-like maps with different kneading sequences from Lozi maps

Application of kneading theory to a new class of maps

Numerical evidence supporting diverse dynamical behaviors

Abstract

We define a broad class of piecewise smooth plane homeomorphisms which have properties similar to the properties of Lozi maps, including the existence of a hyperbolic attractor. We call those maps Lozi-like. For those maps one can apply our previous results on kneading theory for Lozi maps. We show a strong numerical evidence that there exist Lozi-like maps that have kneading sequences different than those of Lozi maps.