Minimal combinatorial models for maps of an interval with a given set of periods
Louis Block, Ethan M. Coven, William Geller, and Kristin Hubner
A combinatorial model for a property of continuous self-maps of a compact interval is a self map $\pi$ of a finite ordered set such that every continuous $\pi$-weakly monotone self-map of a compact interval has that property. We identify the minimal combinatorial models for the property "the set of periods is a given set." Here the word minimal refers to the number of points in the domain of the model. We also identify the minimal permutation models, and in appropriate cases, the minimal combinatorial models for properties involving "horseshoes."