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Dimension and measure of baker-like skew-products of $\boldsymbol{\beta}$-transformations

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  • We consider a generalisation of the baker's transformation, consisting of a skew-product of contractions and a $\beta$-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 [12]. This transversality, which is applicable to the considered class of maps holds for a larger set of parameters than Solomyak's transversality.
    Mathematics Subject Classification: Primary: 37D50, 37C40, 37C45.

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