Symbolic partition in chaotic maps

TL;DR

This paper introduces a method for locating partition boundaries in chaotic maps using unstable manifold data, validated on Henon and 3D maps, with results confirmed by Lyapunov exponents and entropy measures.

Contribution

The paper presents a novel approach to identify symbolic partitions in chaotic systems using folding points and homoclinic tangencies, applicable to higher-dimensional maps.

Findings

Partition boundaries coincide with homoclinic tangencies.

Method successfully applied to Henon and 3D maps.

Lyapunov exponents validated through metric entropy.

Abstract

In this work, we only use data on the unstable manifold to locate the partition boundaries by checking folding points at different levels, which practically coincide with homoclinic tangencies (HTs). The method is then applied to the classic two-dimensional Henon map and a well-known three-dimensional map. Comparison with previous results is made in the Henon case and Lyapunov exponents are computed through the metric entropy based on the partition, to show the validity of the current scheme.