# Symbolic dynamics of a piecewise rotation: case of the non symmetric bijective maps

## TL;DR

This paper analyzes the symbolic dynamics of a specific non-symmetric piecewise rotation of the plane for certain angles, providing a complete description in the bijective case.

## Contribution

It offers a comprehensive analysis of the symbolic dynamics for non-symmetric bijective piecewise rotations at specific angles, extending previous studies.

## Key findings

- Complete symbolic dynamics descriptions for angles π/2, 2π/3, π/4
- Characterization of non-symmetric bijective maps
- Extension of prior work on piecewise rotations

## Abstract

We consider a specific piecewise rotation of the plane that is continuous on two half-planes, as studied by some authors like Boshernitzan, Goetz and Quas. If the angle belongs to the set $\{\frac{\pi}{2},\frac{2\pi}{3},\frac{\pi}{4}\}$, we give a complete description of the symbolic dynamics of this map in the non symmetric bijective case.