Increasing digit subsystems of infinite iterated function systems

Thomas M Jordan; Michal Rams

doi:10.1090/S0002-9939-2011-10969-9

Increasing digit subsystems of infinite iterated function systems

Thomas M Jordan
, Michal Rams

Research output: Contribution to journal › Article (Academic Journal) › peer-review

32 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 contribution	Increasing digit subsystems of infinite iterated function systems
Original language	English
Pages (from-to)	1267-1279
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	140
Issue number	4
Early online date	19 Jul 2011
DOIs	https://doi.org/10.1090/S0002-9939-2011-10969-9
Publication status	Published - 2012

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title = "Increasing digit subsystems of infinite iterated function systems",

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 . ",

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T1 - Increasing digit subsystems of infinite iterated function systems

AU - Jordan, Thomas M

AU - Rams, Michal

PY - 2012

Y1 - 2012

N2 - 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 .

AB - 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 .

U2 - 10.1090/S0002-9939-2011-10969-9

DO - 10.1090/S0002-9939-2011-10969-9

M3 - Article (Academic Journal)

SN - 0002-9939

VL - 140

SP - 1267

EP - 1279

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -

Increasing digit subsystems of infinite iterated function systems

Abstract

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