Topological orbit equivalence classes and numeration scales of logistic maps

TL;DR

This paper demonstrates that all uniquely ergodic minimal Cantor systems are topologically orbit equivalent to extensions of numeration scales derived from logistic maps, linking dynamical systems and number theory.

Contribution

It establishes a novel connection between minimal Cantor systems and logistic map numeration scales through topological orbit equivalence.

Findings

Every uniquely ergodic minimal Cantor system is topologically orbit equivalent to a logistic map extension.

Provides a new classification framework linking Cantor systems and logistic map numeration.

Enhances understanding of the structure of minimal dynamical systems.

Abstract

We show that every uniquely ergodic minimal Cantor system is topological orbit equivalent to the natural extension of a numeration scale associated to a logistic map.