# Homeomorphisms of unimodal inverse limit spaces with a non-recurrent postcritical point

## TL;DR

This paper proves that for non-recurrent tent map inverse limit spaces, all homeomorphisms are essentially shifts, showing the automorphism group is very simple.

## Contribution

It establishes that every homeomorphism in these spaces is isotopic to a power of the shift, revealing the automorphism group's simplicity.

## Key findings

- All homeomorphisms are isotopic to shift powers
- Automorphism group is very simple
- Homeomorphisms preserve the inverse limit structure

## Abstract

In this paper we show that the group of automorphisms of a non-recurrent tent map inverse limit is very simple by demonstrating that every homeomorphism of such a space is isotopic to a power of the induced shift homeomorphism.