Folding and Metric Entropies for Extended Shifts
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908794669236224 |
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| author | Martins, Neemias Mattos, Pedro G. Varão, Régis |
| author_facet | Martins, Neemias Mattos, Pedro G. Varão, Régis |
| contents | In this paper we calculate the metric and folding entropies for a family of non-invertible symbolic dynamical systems $(Σ_{m_-,m_+}, σ_ϕ)$ which generalizes the standard bilateral Bernoulli shifts. The space $Σ_{m_-,m_+}$ consists of symbolic sequences over two distinct finite alphabets, with dynamics governed by a shift map $σ_ϕ$ incorporating a non-invertible function $ϕ$ that maps one of the alphabets to the other one. These systems are, for instance, particularly useful for encoding the many-to-one baker's transformation endomorphisms, and they can also be seen as a skew product with a unilateral Bernoulli shift on the base. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01828 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Folding and Metric Entropies for Extended Shifts Martins, Neemias Mattos, Pedro G. Varão, Régis Dynamical Systems 37A35 (Primary), 37B10 (Secondary) In this paper we calculate the metric and folding entropies for a family of non-invertible symbolic dynamical systems $(Σ_{m_-,m_+}, σ_ϕ)$ which generalizes the standard bilateral Bernoulli shifts. The space $Σ_{m_-,m_+}$ consists of symbolic sequences over two distinct finite alphabets, with dynamics governed by a shift map $σ_ϕ$ incorporating a non-invertible function $ϕ$ that maps one of the alphabets to the other one. These systems are, for instance, particularly useful for encoding the many-to-one baker's transformation endomorphisms, and they can also be seen as a skew product with a unilateral Bernoulli shift on the base. |
| title | Folding and Metric Entropies for Extended Shifts |
| topic | Dynamical Systems 37A35 (Primary), 37B10 (Secondary) |
| url | https://arxiv.org/abs/2407.01828 |