Quasi-Assouad dimension of fractals

  • Fan Lü

    Sichuan Normal University, Chengdu, China
  • Li-Feng Xi

    Ningbo University, China

Abstract

The Assouad dimension of fractals is not invariant under quasi-Lipschitz mappings, even for Ahlfors–David regular sets. In this manuscript, we shall give a new dimension dim of fractals named the quasi-Assouad dimension, which is invariant under any quasi-Lipschitz mapping, satisfying for any compact subset of a metric space. By virtue of the quasi-Assouad dimension, we show that any Bedford–McMullen carpet is quasi-Lipschitz Assouad-minimal, i.e., dim for any quasi-Lipschitz mapping .

Cite this article

Fan Lü, Li-Feng Xi, Quasi-Assouad dimension of fractals. J. Fractal Geom. 3 (2016), no. 2, pp. 187–215

DOI 10.4171/JFG/34