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Abstract
The intermediate dimensions of a set Λ\LambdaΛ, elsewhere denoted by dimθΛ\dim_{\theta}\LambdadimθΛ, interpolate between its Hausdorff and box dimensions using the parameter θ∈[0,1]\theta\in[0,1]θ∈[0,1]. For a Bedford–McMullen carpet Λ\LambdaΛ with distinct Hausdorff and box dimensions, we show that dimθΛ\dim_{\theta}\LambdadimθΛ is strictly less than the box dimension of Λ\LambdaΛ for every θ<1\theta<1θ<1. Moreover, the derivative of the upper bound is strictly positive at θ=1\theta=1θ=1. This answers a question of Fraser; however, determining a precise formula for dimθΛ\dim_{\theta}\LambdadimθΛ still remains a challenging problem.
Original language  English 

Pages (fromto)  151169 
Number of pages  19 
Journal  Journal of Fractal Geometry 
Volume  9 
Issue number  12 
DOIs  
Publication status  Published  11 Jul 2022 
Keywords
 Intermediate dimensions
 BedfordMcMullen carpet
 Hausdorff dimension
 Box dimension
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Dive into the research topics of 'An upper bound for the intermediate dimensions of Bedford–McMullen carpets'. Together they form a unique fingerprint.Projects
 1 Finished

New perspectives in the dimension: New perspectives in the dimension theory of fractals
1/09/19 → 31/01/23
Project: Standard