Geodesic
Inhomogeneous self-similar sets and box dimensions
Jonathan M. Fraser1
1 Mathematical Institute University of St Andrews North Haugh St Andrews, Fife, KY16 9SS, Scotland
Studia Mathematica, Tome 213 (2012) no. 2, pp. 133-156 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm213-2-2
Keywords: investigate box dimensions inhomogeneous self similar sets firstly extend results olsen snigireva computing upper box dimensions assuming mild separation conditions secondly investigate difficult problem computing lower box dimension non trivial bounds provide examples lower box dimension behaves much strangely upper box dimension hausdorff dimension packing dimension

Jonathan M. Fraser 1

1 Mathematical Institute University of St Andrews North Haugh St Andrews, Fife, KY16 9SS, Scotland 
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Jonathan M. Fraser. Inhomogeneous self-similar sets and box dimensions. Studia Mathematica, Tome 213 (2012) no. 2, pp. 133-156. doi: 10.4064/sm213-2-2

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