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An elementary proof that the Rauzy gasket is fractal

Part of: Classical measure theory

Published online by Cambridge University Press:  25 September 2023

MARK POLLICOTT  and
BENEDICT SEWELL
MARK POLLICOTT
Affiliation:
Mathematics Department, University of Warwick, Coventry CV4 7AL, UK (e-mail: masdbl@warwick.ac.uk)
BENEDICT SEWELL*
Affiliation:
Alfréd Rényi Institute, 13–15 Reáltonoda utca, Budapest 1053, Hungary
*
e-mail: sewell@renyi.hu
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Abstract

We present an elementary proof that the Rauzy gasket has Hausdorff dimension strictly smaller than two.

Keywords

Rauzy gasketHausdorff dimensionself-projective attractorsprojective iterated function systems

MSC classification

Primary: 28A80: Fractals
Secondary: 28A78: Hausdorff and packing measures
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , First View , pp. 1 - 10
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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