Fractal dimensions of subfractals induced by sofic subshifts

TL;DR

This paper investigates the fractal dimensions of subfractals generated by hyperbolic iterated function systems constrained by sofic subshifts, establishing bounds via topological pressure functions.

Contribution

It introduces bounds for various fractal dimensions of subfractals associated with sofic subshifts using topological pressure analysis.

Findings

Zeros of pressure functions bound fractal dimensions

Hausdorff and packing dimensions are estimated

Provides a method to analyze subfractals in symbolic dynamics

Abstract

In this paper, we will consider subfractals of hyperbolic iterated function systems which satisfy the open set condition. The subfractals will consist of points associated with infinite strings from a subshift of finite type or sofic subshift on the symbolic space. We find that the zeros of the lower and upper topological pressure functions are lower and upper bounds, respectively, for the Hausdorff, packing, lower and upper box dimensions of the subfractal.