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Global rigidity of smooth ${\mathbb Z}\ltimes_λ{\mathbb R}$-actions on ${\mathbb T}^2$ (2403.10060v1)
Published 15 Mar 2024 in math.DS
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 $Cr$ 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.