Hetero-dimensional baker maps and Dyck shifts

TL;DR

This paper introduces piecewise affine maps on the unit cube that encode the Dyck shift symbolically, providing a novel approach to analyze the system's chaotic behavior and compute its entropy.

Contribution

It presents a new method of representing the Dyck shift through affine maps, offering an alternative way to verify chaos and calculate entropy.

Findings

Established a piecewise affine map representation of the Dyck shift

Provided a new approach to verify chaos in the system

Computed the entropy of the system using the new representation

Abstract

We give piecewise affine maps on the unit cube whose symbolic representation is the Dyck shift. This leads to a different way of verifying the chaotic nature of this system, including the computation of entropy.