# Non-homogeneous extensions of Cantor minimal systems

## TL;DR

This paper extends the class of minimal dynamical systems by generalizing fibers from intervals to higher-dimensional cubes and attractors of iterated function systems, broadening the scope of Cantor minimal systems.

## Contribution

It introduces non-homogeneous extensions of Cantor minimal systems with fibers as higher-dimensional cubes and attractors, expanding previous models.

## Key findings

- Fibers can be generalized to higher-dimensional cubes.
- Attractors of certain iterated function systems can serve as fibers.
- Applications of these generalized systems are discussed.

## Abstract

Floyd gave an example of a minimal dynamical system which was an extension of an odometer and the fibres of the associated factor map were either singletons or intervals. Gjerde and Johansen showed that the odometer could be replaced by any Cantor minimal system. Here, we show further that the intervals can be generalized to cubes of arbitrary dimension and to attractors of certain iterated function systems. We discuss applications.