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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.14753 |
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| _version_ | 1866915865224544256 |
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| author | Ures, Raul Yu, Tongyao |
| author_facet | Ures, Raul Yu, Tongyao |
| contents | We show that for $n\ge2$, if a partially hyperbolic diffeomorphism $f:\mathbb T^{n+1}\to \mathbb T^{n+1}$ with $\dim E^s=\dim E^c=1$ has an invariant center-unstable foliation with a compact incompressible leaf, then this foliation has a transverse closed curve in the universal cover. Also, if $f$ is leaf conjugate to its linear part, it has no compact incompressible center-unstable submanifold. In particular, by the incompressibility result we obtained on Anosov tori, the incompressibility assumptions can be removed when $f$ is defined on $\mathbb T^4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14753 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Partially Hyperbolic Dynamics on $\mathbb T^4$: Existence of Compact Center-Unstable Leaves Ures, Raul Yu, Tongyao Dynamical Systems We show that for $n\ge2$, if a partially hyperbolic diffeomorphism $f:\mathbb T^{n+1}\to \mathbb T^{n+1}$ with $\dim E^s=\dim E^c=1$ has an invariant center-unstable foliation with a compact incompressible leaf, then this foliation has a transverse closed curve in the universal cover. Also, if $f$ is leaf conjugate to its linear part, it has no compact incompressible center-unstable submanifold. In particular, by the incompressibility result we obtained on Anosov tori, the incompressibility assumptions can be removed when $f$ is defined on $\mathbb T^4$. |
| title | Partially Hyperbolic Dynamics on $\mathbb T^4$: Existence of Compact Center-Unstable Leaves |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2603.14753 |