Work

Fractal tiles induced by tent maps

Year: 2025

Type: article

Abstract: In the present article, we deal with geometrical objects induced by the tent maps associated with special Pisot numbers that we call tent-tiles. They are compact subsets of one-, two-, or three-dimensional Euclidean space, depending on the particular special Pisot number. Most of the tent-tiles have a fractal shape and we study the Hausdorff dimension of their boundary. Furthermore, we are concerned with tilings induced by tent-tiles. It turns out that tent-tiles give rise to two types of lattice tilings. In order to obtain these results, we establish and exploit connections between tent-tiles and Rauzy fractals induced by substitutions and automorphisms of the free group.

Source: Discrete and Continuous Dynamical Systems

DOI: 10.3934/dcds.2025160

Authors: Klaus Scheicher, Víctor F. Sirvent, Paul Surer

Institutions: BOKU University, Universidad Católica del Norte

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Austrian Science Fund

Award: Generalised number systems and the dynamics beyond