Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T04:26:37.913Z Has data issue: false hasContentIssue false
  • English
  • Français

Computing the dimension of dynamically defined sets: E_2 and bounded continued fractions

Published online by Cambridge University Press:  02 October 2001

OLIVER JENKINSON  and
MARK POLLICOTT
OLIVER JENKINSON
Affiliation:
UPR 9016 CNRS, Institut de Mathématiques de Luminy, 163 avenue de Luminy, case 907, 13288 Marseille, cedex 9, France (e-mail: [email protected]) Present address: School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK
MARK POLLICOTT
Affiliation:
Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a powerful approach to computing the Hausdorff dimension of certain conformally self-similar sets. We illustrate this method for the dimension \mathop{\rm dim}\nolimits_H(E_2) of the set E_2, consisting of those real numbers whose continued fraction expansions contain only the digits 1 or 2. A very striking feature of this method is that the successive approximations converge to \mathop{\rm dim}\nolimits_H(E_2) at a super-exponential rate

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 5 , October 2001 , pp. 1429 - 1445
Copyright
2001 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)