A formula for the upper box-counting dimension of self-projective sets

2023/06/05 by Sewell, Benedict
#28A78 #28A80 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.03047

Abstract

We prove a packing exponent formula for the upper box-counting dimension of attractors of certain projective iterated function systems. This partially affirms a conjecture of De Leo, and gives that the box-counting dimension of the Rauzy gasket \mathcal R, dim_B(\mathcal R), exists and satisfies dim_B(\mathcal R) = dim_H(\mathcal R) ∈ [1.6196,1.7415].

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