Language of a non-minimal billiard trajectory inside a cube

TL;DR

This paper investigates the symbolic coding of non-minimal billiard trajectories inside a cube, analyzing the language generated by orbits when mapped to three non-parallel faces.

Contribution

It introduces a new analysis of the symbolic language of billiard trajectories in a cube, focusing on non-minimal orbits and their coding with three face-associated symbols.

Findings

Characterization of the language of non-minimal billiard trajectories

Identification of properties of the symbolic sequences

Insights into the structure of orbit coding in three-face mappings

Abstract

We consider a non-minimal billiard trajectory inside the cube. We study the language of the associated orbit when the map is coded with three letters associated to three non-parallel faces of the cube.