Hausdorff dimension of the parameters for $(α,β)$-transformations with the specification property
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929284428333056 |
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| author | Oguchi, Mai Shinoda, Mao |
| author_facet | Oguchi, Mai Shinoda, Mao |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_14230 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hausdorff dimension of the parameters for $(α,β)$-transformations with the specification property Oguchi, Mai Shinoda, Mao Dynamical Systems 37E45, 37E05, 11K55 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. |
| title | Hausdorff dimension of the parameters for $(α,β)$-transformations with the specification property |
| topic | Dynamical Systems 37E45, 37E05, 11K55 |
| url | https://arxiv.org/abs/2403.14230 |