# Edrei's Conjecture revisited

## TL;DR

This paper explores the dynamics of certain minimal systems, providing new counterexamples to Edrei's conjecture by analyzing systems conjugate to those with vanishing derivatives, revealing diverse behaviors.

## Contribution

It introduces new counterexamples to Edrei's conjecture by studying systems conjugate to those with vanishing derivatives and locally radially shrinking maps.

## Key findings

- Discovered a spectrum of dynamical behaviors in such systems
- Provided new counterexamples to Edrei's 1952 conjecture
- Extended understanding of minimal dynamical systems with special properties

## Abstract

Motivated by a recent result of Ciesielski and Jasinski we study periodic point free Cantor systems that are conjugate to systems with vanishing derivative everywhere, and more generally locally radially shrinking maps. Our study uncovers a whole spectrum of dynamical behaviors attainable for such systems, providing new counterexamples to the Conjecture of Edrei from 1952, first disproved by Williams in 1954.