Let be the solvable Baumslag–Solitar group, where . It is known that is isomorphic to the group generated by the two affine maps of the line: and . The action on generated by these two affine maps and is called the standard affine one. We prove that any faithful representation of into is semiconjugated (up to a finite index subgroup) to the standard affine action.
"$C^1$–actions of Baumslag–Solitar groups on $S^1$." Algebr. Geom. Topol. 11 (3) 1701 - 1707, 2011. https://doi.org/10.2140/agt.2011.11.1701