Global rigidity of smooth ${\mathbb Z}\ltimes_λ{\mathbb R}$-actions on ${\mathbb T}^2$
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913266132844544 |
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| author | Dong, Changguang Shi, Yi |
| author_facet | Dong, Changguang Shi, Yi |
| contents | For $λ>1$, we consider the locally free ${\mathbb Z}\ltimes_λ{\mathbb R}$ actions on ${\mathbb T}^2$. We show that, if the action is $C^r$ with $r\geq2$, then it is $C^{r-ε}$-conjugate to an affine action generated by a hyperbolic automorphism and a linear translation flow along expanding eigen-direction of the automorphism. In contrast, there exists a $C^{1+α}$-action which is semi-conjugate, but not topologically conjugate to an affine action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10060 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global rigidity of smooth ${\mathbb Z}\ltimes_λ{\mathbb R}$-actions on ${\mathbb T}^2$ Dong, Changguang Shi, Yi Dynamical Systems For $λ>1$, we consider the locally free ${\mathbb Z}\ltimes_λ{\mathbb R}$ actions on ${\mathbb T}^2$. We show that, if the action is $C^r$ with $r\geq2$, then it is $C^{r-ε}$-conjugate to an affine action generated by a hyperbolic automorphism and a linear translation flow along expanding eigen-direction of the automorphism. In contrast, there exists a $C^{1+α}$-action which is semi-conjugate, but not topologically conjugate to an affine action. |
| title | Global rigidity of smooth ${\mathbb Z}\ltimes_λ{\mathbb R}$-actions on ${\mathbb T}^2$ |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2403.10060 |