Dimension and measure of baker-like skew-products of β-transformations

2010/04/27 by Färm, David, Persson, Tomas
#37C40 #37C45 #37D50 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1004.4814

Abstract

We consider a generalisation of the baker's transformation, consisting of a skew-product of contractions and a β-transformation. The Hausdorff dimension and Lebesgue measure of the attractor is calculated for a set of parameters with positive measure. The proofs use a new transverality lemma similar to Solomyak's [Solomyak, 1995]. This transversality, which is applicable to the considered class of maps holds for a larger set of parameters than Solomyak's transversality.

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