Furstenberg counterexamples over Diophantine rotations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915057133158400 |
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| author | Karaliolios, Nikolaos |
| author_facet | Karaliolios, Nikolaos |
| contents | We construct cocycles in $\mathbb{T} \times SU(2)$ over Diophantine rotations that are minimal and not uniquely ergodic. Such cocycles are dense in an open subset of cocycles over the fixed Diophantine rotation. By a standard argument, they are dense in the whole set of such cocycles if the rotation satisfies a full-measure arithmetic condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07484 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Furstenberg counterexamples over Diophantine rotations Karaliolios, Nikolaos Dynamical Systems 37C55, 37A30 We construct cocycles in $\mathbb{T} \times SU(2)$ over Diophantine rotations that are minimal and not uniquely ergodic. Such cocycles are dense in an open subset of cocycles over the fixed Diophantine rotation. By a standard argument, they are dense in the whole set of such cocycles if the rotation satisfies a full-measure arithmetic condition. |
| title | Furstenberg counterexamples over Diophantine rotations |
| topic | Dynamical Systems 37C55, 37A30 |
| url | https://arxiv.org/abs/2412.07484 |