Minimal Riesz energy on balanced fractal sets

Abstract

We investigate the asymptotic behavior of minimal N-point Riesz s-energy on fractal sets of non-integer dimension, with algebraically dependent contraction ratios. For s bigger than the dimension of the set A, we prove the asymptotic behavior of the minimal N-point Riesz s-energy of A along explicit subsequences, but we show that the general asymptotic behavior does not exist.