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Global rigidity of smooth ${\mathbb Z}\ltimes_\lambda{\mathbb R}$-actions on ${\mathbb T}^2$
- Publication Year :
- 2024
-
Abstract
- For $\lambda>1$, we consider the locally free ${\mathbb Z}\ltimes_\lambda{\mathbb R}$ actions on ${\mathbb T}^2$. We show that, if the action is $C^r$ with $r\geq2$, then it is $C^{r-\epsilon}$-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 $C^{1+\alpha}$-action which is semi-conjugate, but not topologically conjugate to an affine action.
- Subjects :
- Mathematics - Dynamical Systems
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2403.10060
- Document Type :
- Working Paper