Spectral orthogonality of special flows
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911287273848832 |
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| author | Sheng, Mingcheng |
| author_facet | Sheng, Mingcheng |
| contents | In this paper, we study the spectral orthogonality problem for special flows built over irrational rotations under two different types of roof functions:
1) the roof functions are real analytic.
2) the roof functions are piecewise $C^1$ with one discontinuity. These flows are also known as von-Neumann flows.
We show that if $\{T^f_α\}$ is as in 1) and weak mixing, then for a $G_δ$ dense set of $β$, we have that $\{T^f_β\}$ is weak-mixing and is spectrally orthogonal to $\{T^f_α\}$. On the other hand, if $\{T^f_α\}$ is as in 2), then for a full measure set of $β$, the flows $\{T^f_α\}$ and $\{T^f_β\}$ are spectrally orthogonal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20825 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral orthogonality of special flows Sheng, Mingcheng Dynamical Systems In this paper, we study the spectral orthogonality problem for special flows built over irrational rotations under two different types of roof functions: 1) the roof functions are real analytic. 2) the roof functions are piecewise $C^1$ with one discontinuity. These flows are also known as von-Neumann flows. We show that if $\{T^f_α\}$ is as in 1) and weak mixing, then for a $G_δ$ dense set of $β$, we have that $\{T^f_β\}$ is weak-mixing and is spectrally orthogonal to $\{T^f_α\}$. On the other hand, if $\{T^f_α\}$ is as in 2), then for a full measure set of $β$, the flows $\{T^f_α\}$ and $\{T^f_β\}$ are spectrally orthogonal. |
| title | Spectral orthogonality of special flows |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2511.20825 |