Conformal iterated function systems with applications to the geometry of continued fractions

Transactions of the American Mathematical Society

Volumn 351, Issue 12, 1999, Pages 4995-5025

  Daniel Mauldin, R ^a   Urbański, Mariusz ^a  

^a UNIVERSITY OF NORTH TEXAS   (United States)

Author keywords

Arithmetic densities; Continued fractions; Hausdorff and oackine measures; Hausdorff dimension; Iterated function systems

Indexed keywords

EID: 22844455461     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (8)

1. [Cu] T.W. Cusick, Hausdorff dimension of sets of continued fractions, Quart. J. Math. Oxford (2), 41 (1990), 277-286. MR 91m:11057
2. [B] P. Erdös, On the difference of consecutive primes, Quart. J. Oxford 6 (1935), 124-128.
3. [Go] I.J. Good, The fractional dimension theory of continued fractions, Proc. Carnb. Philos. Soc. 37(1941), 199-228; Corrigenda, Math. Proc. Camb. Phil. Soc. 105(1989), 607; Addenda, J. Statist. Cpmput. and Simul. 32, Nos. 1-2 (1989), 64-68. MR 3:7b; MR 90i:28013
4. [He] D. Hensley, Continued fraction Cantor sets, Hausdorff dimension, and functional analysis, J. Number Th. 40(1992), 336-358. MR 93c:11058
5. [M] H. Maier, Chains of large gaps between consecutive primes, Advances Math. 39 (1981), 257-269. MR 82g:10061
6. [Ma] P. Mattila, Geometry of sets and measures in euclidean spaces, Cambridge Studies in Advanced Mathematics 44(Cambridge University Press, 1995). MR 96h:28006
7. [MU] R.D. Mauldin, M. Urbanski, Dimensions and measures in infinite iterated function systems, Proceedings London Math. Soc., (3) 73(1996), 105-154. MR 97c:28020
8. [Ra] G. Ramharter, Some metrical properties of continued fractions, Mathematika 30 (1983), 117-132. MR 85c:11058