Increasing digit subsystems of infinite iterated function systems

Authors:
Thomas Jordan and Michał Rams

Journal:
Proc. Amer. Math. Soc. **140** (2012), 1267-1279

MSC (2010):
Primary 28A80; Secondary 11K50

Published electronically:
July 19, 2011

MathSciNet review:
2869111

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**Thomas Jordan**

Affiliation:
School of Mathematics, The University of Bristol, University Walk, Clifton, Bristol, BS8 1TW, United Kingdom

Email:
thomas.jordan@bristol.ac.uk

**Michał Rams**

Affiliation:
Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-956 Warszawa, Poland

Email:
M.Rams@impan.gov.pl

DOI:
http://dx.doi.org/10.1090/S0002-9939-2011-10969-9

Received by editor(s):
October 25, 2010

Received by editor(s) in revised form:
December 21, 2010

Published electronically:
July 19, 2011

Additional Notes:
The second author’s research was supported by grants EU FP6 ToK SPADE2, EU FP6 RTN CODY and MNiSW grant ‘Chaos, fraktale i dynamika konforemna’.

Communicated by:
Bryna Kra

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.