Increasing digit subsystems of infinite iterated function systems

Thomas M Jordan, Michal Rams

Research output: Contribution to journalArticle (Academic Journal)peer-review

12 Citations (Scopus)

Abstract

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 contributionIncreasing digit subsystems of infinite iterated function systems
Original languageEnglish
Pages (from-to)1267-1279
Number of pages13
JournalProceedings of the American Mathematical Society
Volume140
Issue number4
Early online date19 Jul 2011
DOIs
Publication statusPublished - 2012

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