Local smooth rigidity of Anosov diffeomorphisms in $\mathbb{T}^{3}$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908924103360512 |
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| author | Reber, James Marshall Pavez-Molina, Sebastián |
| author_facet | Reber, James Marshall Pavez-Molina, Sebastián |
| contents | Given a $C^0$ conjugacy between two Anosov diffeomorphisms, the matching periodic data problem asks whether this conjugacy is smooth provided spectral data of the diffeomorphisms match at periodic points. We show that if the two $C^0$ conjugate diffeomorphisms on $\mathbb{T}^3$ are sufficiently close to a hyperbolic linear automorphism with a pair of complex conjugate eigenvalues, then the conjugacy must be smooth. In particular, we have that in a neighborhood of a hyperbolic toral automorphism, matching periodic data implies that the conjugacy is $C^{1+\text{Hölder}}$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29155 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local smooth rigidity of Anosov diffeomorphisms in $\mathbb{T}^{3}$ Reber, James Marshall Pavez-Molina, Sebastián Dynamical Systems 37C15, 37D20 Given a $C^0$ conjugacy between two Anosov diffeomorphisms, the matching periodic data problem asks whether this conjugacy is smooth provided spectral data of the diffeomorphisms match at periodic points. We show that if the two $C^0$ conjugate diffeomorphisms on $\mathbb{T}^3$ are sufficiently close to a hyperbolic linear automorphism with a pair of complex conjugate eigenvalues, then the conjugacy must be smooth. In particular, we have that in a neighborhood of a hyperbolic toral automorphism, matching periodic data implies that the conjugacy is $C^{1+\text{Hölder}}$ |
| title | Local smooth rigidity of Anosov diffeomorphisms in $\mathbb{T}^{3}$ |
| topic | Dynamical Systems 37C15, 37D20 |
| url | https://arxiv.org/abs/2603.29155 |