Rigidity for $C^1$ actions on the interval arising from hyperbolicity I: solvable groups

C. Bonatti, I. Monteverde, A. Navas +1

We consider Abelian-by-cyclic groups for which the cyclic factor acts by hyperbolic automorphisms on the Abelian subgroup. We show that if such a group acts faithfully by $C^1$ dif…