Rigidity for $$C^1$$C1 actions on the interval arising from hyperbolicity I: solvable groups

@article{Bonatti2013RigidityF,
  title={Rigidity for \$\$C^1\$\$C1 actions on the interval arising from hyperbolicity I: solvable groups},
  author={Ch. Bonatti and Ignacio Monteverde and Andr{\'e}s Navas and Crist{\'o}bal Rivas},
  journal={Mathematische Zeitschrift},
  year={2013},
  volume={286},
  pages={919-949}
}
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 $$C^1$$C1 diffeomorphisms of the closed interval with no global fixed point at the interior, then the action is topologically conjugate to that of an affine group. Moreover, in case of non-Abelian image, we show a rigidity result concerning the multipliers of the homotheties, despite the fact that the conjugacy is not… CONTINUE READING
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