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

David Färm; Tomas Persson

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

Dynamical Systems 2015-03-17 v2

Authors: David Färm , Tomas Persson

Abstract

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 [Solomyak, 1995]. This transversality, which is applicable to the considered class of maps holds for a larger set of parameters than Solomyak's transversality.

Keywords

baker-like skew-products beta-transformations hausdorff dimension lebesgue measure attractor transversality lemma

Cite

@article{arxiv.1004.4814,
  title  = {Dimension and measure of baker-like skew-products of $\beta$-transformations},
  author = {David Färm and Tomas Persson},
  journal= {arXiv preprint arXiv:1004.4814},
  year   = {2015}
}

Comments

14 pages, 3 figures. Some typos have been corrected, and some arguments have been written out in greater details

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

Abstract

Keywords

Cite

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