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arXiv · 2403.14230

Hausdorff dimension of the parameters for $(α,β)$-transformations with the specification property

Mai Oguchi·Mao Shinoda
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Abstract

In this paper we consider the specification property for $(α,β)$-shifts. When $α=0$, Schmeling shows that the set of $β>1$ for which the $β$-shift has the specification property has the Lebesgue measure zero but has the full Hausdorff dimension\cite{Schmeling}. So it is natural to ask what happens when $α>0$. Buzzi shows that for fixed $α$ the set of $β>1$ for which the $(α,β)$-shift has the specification property has Lebesgue measure zero. Hence we consider the Hausdorff dimension of the parameter space of $(α,β)$-shifts.

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Mai Oguchi, Mao Shinoda. 2024-03-21. Hausdorff dimension of the parameters for $(α,β)$-transformations with the specification property. https://arxiv.org/abs/2403.14230

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