Unbounded orbits for the Plaid Model

TL;DR

This paper proves that the plaid model contains unbounded polygonal paths for all irrational parameters, extending previous work on outer billiards on kites and demonstrating unbounded orbits in this dynamical system.

Contribution

It establishes the existence of unbounded orbits in the plaid model for all irrational parameters, a novel result linking it to outer billiards dynamics.

Findings

Unbounded polygonal paths exist for all irrational parameters in the plaid model.

The result parallels unbounded orbits in outer billiards on kites.

Confirms the unbounded nature of the plaid model's trajectories for irrational parameters.

Abstract

This paper is a sequel to my paper "Introducing the Plaid Model". In this paper it is shown that the plaid model has unbounded polygonal paths for every irrational parameter. This result parallels my result that outer billiards on kites has unbounded orbits for every irrational parameter