Hausdorff Dimension Spectrum of Self-Affine Carpets Indexed by Nonlinear Fibre-Coding

摘要

In this paper we study a class of subsets of self-affine carpets which are indexed by fibre-coding, but their limiting frequencies have nonlinear relation. We obtain their Hausdorff dimension spectrum and give the necessary and sufficient conditions of these fractal sets to be s-set.