Inhomogeneous self-similar sets and box dimensions

• Autorzy: Jonathan M. Fraser
• Języki publikacji: EN

Abstrakty

EN

We investigate the box dimensions of inhomogeneous self-similar sets. Firstly, we extend some results of Olsen and Snigireva by computing the upper box dimensions assuming some mild separation conditions. Secondly, we investigate the more difficult problem of computing the lower box dimension. We give some non-trivial bounds and provide examples to show that lower box dimension behaves much more strangely than upper box dimension, Hausdorff dimension and packing dimension.

Kategorie tematyczne

• 26A18: Iteration
• 28A80: Fractals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 213
• Numer: 2
• Strony: 133-156

Daty

wydano

2012

Twórcy

autor

Jonathan M. Fraser

• Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland

Identyfikatory

DOI

10.4064/sm213-2-2