The intermediate dimensions of a set Λ, elsewhere denoted by dim_θ Λ, interpolate between its Hausdorff and box dimensions using the parameter θ ∈ [0,1]. Determining a precise formula for dim_θ Λ is particularly challenging when Λ is a Bedford-McMullen carpet with distinct Hausdorff and box dimension. In this talk, after giving an overview on dimension interpolation, we will present an argument that shows that dim_θ Λ is strictly less than the box dimension of Λ for every θ < 1. Time permitting, we will also show how to improve on the lower bound obtained by Falconer, Fraser, and Kempton.
On the intermediate dimensions of Bedford-McMullen carpets
12.11.2020 17:15 - 18:45
Organiser:
H. Bruin, R. Zweimüller
Location:
zoom-meeting