Computing the dimension of dynamically defined sets: E-2 and bounded continued fractions

Authors
Jenkinson, O Pollicott, M
Citation
O. Jenkinson et M. Pollicott, Computing the dimension of dynamically defined sets: E-2 and bounded continued fractions, ERGOD TH DY, 21, 2001, pp. 1429-1445
Citations number
31
Categorie Soggetti
Mathematics
Journal title
ERGODIC THEORY AND DYNAMICAL SYSTEMS
ISSN journal
01433857 → ACNP
Volume
21
Year of publication
2001
Part
5
Pages
1429 - 1445
Database
ISI
SICI code
0143-3857(200110)21:<1429:CTDODD>2.0.ZU;2-X
Abstract
We present a powerful approach to computing the Hausdorff dimension of cert ain conformally self-similar sets. We illustrate this method for the dimens ion dim(H) (E-2) Of the set E-2, consisting of those real numbers whose con tinued fraction expansions contain only the digits 1 or 2. A very striking feature of this method is that the successive approximations converge to di m(H) (E-2) at a super-exponential rate.