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On the Hausdorff dimension of the Rauzy gasket

Artur Avila,Pascal Hubert,Alexandra Skripchenko

BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE（2016）

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Abstract
In this paper, we prove that the Hausdorff dimension of the Rauzy gasket is less than 2. By this result, we answer a question addressed by Pierre Arnoux. Also, this question is a very particular case of the conjecture stated by S.P. Novikov and A. Maltsev in 2003.
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Systems of isometries,Rauzy induction,Hausdorff dimension
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