Polynomial shape adic systems are inherently expansive
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917766175391744 |
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| author | Frick, Sarah Petersen, Karl Shields, Sandi |
| author_facet | Frick, Sarah Petersen, Karl Shields, Sandi |
| contents | To study any dynamical system it is useful to find a partition that allows essentially faithful encoding (injective, up to a small exceptional set) into a subshift. Most topological and measure-theoretic systems can be represented by Bratteli-Vershik (or adic, or BV) systems. So it is natural to ask when can a BV system be encoded essentially faithfully. We show here that for BV diagrams defined by homogeneous positive integer multivariable polynomials, and a wide family of their generalizations, which we call polynomial shape diagrams, for every choice of the edge ordering the coding according to initial path segments of a fixed finite length is injective off of a negligible exceptional set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00762 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polynomial shape adic systems are inherently expansive Frick, Sarah Petersen, Karl Shields, Sandi Dynamical Systems 37B10, 37B02, 28D05 To study any dynamical system it is useful to find a partition that allows essentially faithful encoding (injective, up to a small exceptional set) into a subshift. Most topological and measure-theoretic systems can be represented by Bratteli-Vershik (or adic, or BV) systems. So it is natural to ask when can a BV system be encoded essentially faithfully. We show here that for BV diagrams defined by homogeneous positive integer multivariable polynomials, and a wide family of their generalizations, which we call polynomial shape diagrams, for every choice of the edge ordering the coding according to initial path segments of a fixed finite length is injective off of a negligible exceptional set. |
| title | Polynomial shape adic systems are inherently expansive |
| topic | Dynamical Systems 37B10, 37B02, 28D05 |
| url | https://arxiv.org/abs/2409.00762 |