Symbolic dynamics for Lozi maps

TL;DR

This paper investigates the symbolic dynamics of Lozi maps and their strange attractors, introducing kneading sequences and alternative methods to characterize their complex behavior.

Contribution

It introduces the concept of kneading sequences for Lozi maps and proves they determine the symbolic dynamics, offering new tools for understanding these systems.

Findings

Kneading sequences uniquely determine symbolic dynamics for Lozi maps.

Two additional approaches to analyze Lozi map dynamics are proposed.

The study enhances understanding of the structure of strange attractors in Lozi maps.

Abstract

In this paper we study the family of the Lozi maps $L_{a,b} : {\mathbb R}^2 \to {\mathbb R}^2$, $L_{a,b} = (1 + y - a|x|, bx)$, and their strange attractors $\Lambda_{a,b}$. We introduce the set of kneading sequences for the Lozi map and prove that it determines the symbolic dynamics for that map. We also introduce two other equivalent approaches.