Conjugacies of Expanding Skew Products on $\mathbb{T}^n$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912376212684800 |
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| author | Hemenway, Gregory |
| author_facet | Hemenway, Gregory |
| contents | We show that any equilibrium state for a Hölder potential on the model map $\vec{x} \mapsto d \cdot \vec{x} \mod \mathbb{Z}^n$ on $\mathbb{T}^n$ is conjugate to Lebesgue measure for an invariant expanding skew product of degree $d$. This is a generalization of a result of McMullen to higher dimensions for equilibrium states. We use an approach developed by the author using a family of nonstationary transfer operators for an expanding skew product. We also apply a Markov partition argument to classify invariant probability measures for expanding maps on $\mathbb{T}^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09575 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conjugacies of Expanding Skew Products on $\mathbb{T}^n$ Hemenway, Gregory Dynamical Systems 37D35 (Primary) 37C30 (Secondary) We show that any equilibrium state for a Hölder potential on the model map $\vec{x} \mapsto d \cdot \vec{x} \mod \mathbb{Z}^n$ on $\mathbb{T}^n$ is conjugate to Lebesgue measure for an invariant expanding skew product of degree $d$. This is a generalization of a result of McMullen to higher dimensions for equilibrium states. We use an approach developed by the author using a family of nonstationary transfer operators for an expanding skew product. We also apply a Markov partition argument to classify invariant probability measures for expanding maps on $\mathbb{T}^n$. |
| title | Conjugacies of Expanding Skew Products on $\mathbb{T}^n$ |
| topic | Dynamical Systems 37D35 (Primary) 37C30 (Secondary) |
| url | https://arxiv.org/abs/2505.09575 |