An ergodic automorphism $\bf T$ with singular spectrum of $\bf T^{\otimes n}$ and Lebesgue one of $\bf T^{\otimes (n+1)}$
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916266128703488 |
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| author | Ryzhikov, Valery V. |
| author_facet | Ryzhikov, Valery V. |
| contents | For any natural $n$, and real $α\geq 0$ we construct an ergodic automorphism $T$ such that its tensor powers $T^{\otimes n}$ have singular spectra if $n\leq 1+α/2$, and Lebesgue if $n\, > 1+α/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19959 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An ergodic automorphism $\bf T$ with singular spectrum of $\bf T^{\otimes n}$ and Lebesgue one of $\bf T^{\otimes (n+1)}$ Ryzhikov, Valery V. Dynamical Systems For any natural $n$, and real $α\geq 0$ we construct an ergodic automorphism $T$ such that its tensor powers $T^{\otimes n}$ have singular spectra if $n\leq 1+α/2$, and Lebesgue if $n\, > 1+α/2$. |
| title | An ergodic automorphism $\bf T$ with singular spectrum of $\bf T^{\otimes n}$ and Lebesgue one of $\bf T^{\otimes (n+1)}$ |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2405.19959 |