Lower bounds on the dimension of the Rauzy gasket

2019/02/12 by Rodolfo Gutiérrez-Romo, Gutiérrez-Romo, Rodolfo, Carlos Matheus +1 · 1 citation
Computer Science · Decision Sciences · #Graph Labeling and Dimension Problems #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.1902.04516

Abstract

The Rauzy gasket R is the maximal invariant set of a certain renormalization procedure for special systems of isometries naturally appearing in the context of Novikov's problem in conductivity theory for monocrystals. It was conjectured by Novikov and Maltsev in 2003 that the Hausdorff dimension dim_H(R) of Rauzy gasket is strictly comprised between 1 and 2. In 2016, Avila, Hubert and Skripchenko confirmed that dim_H(R)<2. In this note, we use some results by Cao--Pesin--Zhao in order to show that dim_H(R)>1.19.

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