Fractal attractors induced by \beta-shifts

TL;DR

This paper investigates a class of fractal attractors generated by eta-shifts, demonstrating their mixing properties, entropy, ergodic measures, and calculating their Hausdorff dimension.

Contribution

It introduces a new class of fractal attractors linked to eta-shifts and analyzes their dynamical and geometric properties.

Findings

Systems are mixing with topological entropy log eta

Existence of an ergodic measure of full entropy

Hausdorff dimension of the attractor is determined

Abstract

We describe a class of fractal attractors induced by \beta-shifts. We use a coding by these shifts to show that the systems are mixing with topological entropy log \beta and have an ergodic measure of full entropy. Moreover we determine the Hausdorff dimension of the attractor.