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arXiv · 1004.4814

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

David Färm·Tomas Persson
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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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David Färm, Tomas Persson. 2011-03-30. Dimension and measure of baker-like skew-products of $β$-transformations. https://arxiv.org/abs/1004.4814

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