Renormalization and forcing of horseshoe orbits

TL;DR

This paper investigates the Boyland order of horseshoe orbits, establishing a set of renormalizable orbits where the order matches the unimodal order, focusing on quasi-one-dimensional cases.

Contribution

It introduces a set of renormalizable horseshoe orbits with Boyland order coinciding with the unimodal order, specifically for quasi-one-dimensional orbits.

Findings

Existence of a set of renormalizable horseshoe orbits

Boyland order matches unimodal order for these orbits

Focus on quasi-one-dimensional horseshoe orbits

Abstract

In this paper we deal with the Boyland order of horseshoe orbits. We prove that there exists a set $\mathcal{R}$ of renormalizable horseshoe orbits containing only quasi-one-dimensional ones, that is, for these orbits the Boyland order coincides with the unimodal order.