Symbolic dynamics for the piecewise rotations: Case of the bijective symmetric maps

TL;DR

This paper analyzes the symbolic dynamics of a specific class of bijective symmetric piecewise rotation maps of the plane, focusing on angles like π/2, π/3, π/6, and π/4, extending previous studies.

Contribution

It provides a detailed description of the symbolic dynamics for these symmetric piecewise rotations at particular angles, which was not previously characterized.

Findings

Symbolic dynamics characterized for angles π/2, π/3, π/6, π/4

Extension of previous work on continuous piecewise rotations

New insights into the structure of bijective symmetric maps

Abstract

We consider a specific %piecewise rotation of the plane that is continuous on two half-planes, class of piecewise rotations of the plane that are continuous on two half-planes, as studied in \cite{Bosh.Goet.03}, \cite{Goet.Quas.09} and \cite{Che.Goe.Qua.12}. %If Assuming that the angle belongs to the set $\{\frac{\pi}{2},\frac{\pi}{3},\frac{\pi}{6},\frac{\pi}{4}\} %$ $, we give a description of the symbolic dynamics of this map in the bijective symmetric case.