# Folding points of unimodal inverse limit spaces

## TL;DR

This paper investigates the structure of folding points and endpoints in unimodal inverse limit spaces, classifying different types and establishing conditions for their occurrence, with a focus on tent inverse limits.

## Contribution

It introduces a detailed classification of folding points and endpoints, providing new conditions for their existence and characterizing when folding points coincide with endpoints.

## Key findings

- Identifies three types of end-points: flat, spiral, and nasty.
- Provides conditions for the existence and prevalence of different folding points.
- Characterizes tent inverse limit spaces where folding points equal endpoints.

## Abstract

We study the properties of folding points and endpoints of unimodal inverse limit spaces. We distinguish between non-end folding points and three types of end-points (flat, spiral and nasty) and give conditions for their existence and prevalence. Additionally, we give a characterisation of tent inverse limit spaces for which the set of folding points equals the set of endpoints.