Structure and Spectrum of Nonergodic Nilsystems
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918416204431360 |
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| author | Hernández, Felipe |
| author_facet | Hernández, Felipe |
| contents | We study Host-Kra factors and the spectral type of nilsystems, without assuming ergodicity. In the ergodic case, it is known that the spectral type splits into a discrete component and a Lebesgue component of infinite multiplicity. Our main result extends this decomposition to nonergodic nilsystems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21021 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Structure and Spectrum of Nonergodic Nilsystems Hernández, Felipe Dynamical Systems 37A30 We study Host-Kra factors and the spectral type of nilsystems, without assuming ergodicity. In the ergodic case, it is known that the spectral type splits into a discrete component and a Lebesgue component of infinite multiplicity. Our main result extends this decomposition to nonergodic nilsystems. |
| title | Structure and Spectrum of Nonergodic Nilsystems |
| topic | Dynamical Systems 37A30 |
| url | https://arxiv.org/abs/2602.21021 |