Forcing among exact patterns of triods

Abstract

We obtain a complete characterization of \emph{topologically exact patterns} on \emph{triods}. Based on their \emph{rotation number} $\rho$, these \emph{exact patterns} are grouped into three classes: \emph{slow} ($\rho < \frac{1}{3}$), \emph{fast} ($\rho > \frac{1}{3}$) and \emph{ternary} ($\rho = \frac{1}{3}$). For each category, we derive a \emph{linear ordering} of the set of natural numbers, $\mathbb{N}$ that captures \emph{forcing} between the \emph{patterns}. We also show that each of these orderings is \emph{stable} under perturbations.