# All minimal Cantor systems are slow

## TL;DR

This paper demonstrates that all minimal Cantor systems can be embedded into the real line with a derivative that vanishes everywhere, revealing new insights into their structure and dynamics.

## Contribution

It establishes that every minimal Cantor system can be embedded into the real line with a vanishing derivative, a novel result linking topological dynamics and differentiability.

## Key findings

- All minimal Cantor systems embed in  with zero derivative
- Relations between local shrinking and periodic points are analyzed
- New connections between topological dynamics and differentiability are identified

## Abstract

We show that every (invertible, or noninvertible) minimal Cantor system embeds in $\mathbb{R}$ with vanishing derivative everywhere. We also study relations between local shrinking and periodic points.