\(C^1\)-actions of Baumslag-Solitar groups on \(S^1\) (Q541305)

The solvable Baumslag-Solitar group, \(BS(1,n) = \langle a,b\mid aba^{-1} = b^n\rangle\), \(n\geq 2\), acts in different manners on \(S^1=\mathbb R \cup \infty\). The standard one is the action generated by the two affine maps of \(\mathbb R\): \(f_0(x) = x + 1\) and \(h_0(x) = nx\). The authors prove that any faithful and preserving orientation \(C^1\)-action of \(BS(1,n)\) on \(S^1\) is semiconjugated to the standard one.