THE FRACTAL DIMENSION OF A UNION OF TRINOMIAL ARCS

Abstract

We consider a specific subset Γ of the unit disk that is a countable union of arcs, these arcs being solutions of the equations zn=αzk+1 -α, α∈(0, 1). We will show that the Minkowski dimension of Γ is 3/2. Two intermediate results concern bounds, one for the length of a curve p=f(θ) when f is monotonic and another for the area of the Minkowski sausage of a curve of finite length.