We consider an infinite iterated function system on with a polynomially increasing contraction rate. We look at subsets of such systems where we only allow iterates if for certain increasing functions . We compute both the Hausdorff and packing dimensions of such sets. Our results generalise work of Ramharter which shows that the set of continued fractions with strictly increasing digits has Hausdorff dimension .
|Translated title of the contribution
|Increasing digit subsystems of infinite iterated function systems
|Number of pages
|Proceedings of the American Mathematical Society
|Early online date
|19 Jul 2011
|Published - 2012