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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.08124 |
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| _version_ | 1866929535779340288 |
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| author | Treviño, Rodrigo |
| author_facet | Treviño, Rodrigo |
| contents | For typical properly ordered and minimal Bratteli diagrams $(B,\leq_r)$, it is shown that there are finitely many invariant distributions $\mathcal{D}_i$ which are the only obstructions to solving the cohomological equation $f = u-u\circ ϕ$ for the corresponding adic transformation $ϕ:X_B\rightarrow X_B$ and for $α$-Hölder $f$ with $α$ large enough. These invariant distributions are then used to define cyclic cocycles, a.k.a. traces $τ:K_0(\mathcal{A}_ϕ)\rightarrow \mathbb{R}$ for the crossed product algebra $\mathcal{A}_ϕ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08124 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The cohomological equation and cyclic cocycles for renormalizable minimal Cantor systems Treviño, Rodrigo Dynamical Systems Operator Algebras For typical properly ordered and minimal Bratteli diagrams $(B,\leq_r)$, it is shown that there are finitely many invariant distributions $\mathcal{D}_i$ which are the only obstructions to solving the cohomological equation $f = u-u\circ ϕ$ for the corresponding adic transformation $ϕ:X_B\rightarrow X_B$ and for $α$-Hölder $f$ with $α$ large enough. These invariant distributions are then used to define cyclic cocycles, a.k.a. traces $τ:K_0(\mathcal{A}_ϕ)\rightarrow \mathbb{R}$ for the crossed product algebra $\mathcal{A}_ϕ$. |
| title | The cohomological equation and cyclic cocycles for renormalizable minimal Cantor systems |
| topic | Dynamical Systems Operator Algebras |
| url | https://arxiv.org/abs/2410.08124 |