Rigidity of generalized Veech 1969/Sataev 1975 extensions of rotations

@article{Ferenczi2020RigidityOG,
  title={Rigidity of generalized Veech 1969/Sataev 1975 extensions of rotations},
  author={S{\'e}bastien Ferenczi and Pasacal Hubert},
  journal={Journal d'Analyse Math{\'e}matique},
  year={2020}
}
We look at $d$-point extensions of a rotation of angle $\alpha$ with $r$ marked points, generalizing the examples of Veech 1969 and Sataev 1975, together with the square-tiled interval exchange transformations of \cite{fh2}. We study the property of rigidity, in function of the Ostrowski expansions of the marked points by $\alpha$: we prove that $T$ is rigid when $\alpha$ has unbounded partial quotients, and that $T$ is not rigid when the natural coding of the underlying rotation with marked… 

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