Corpus ID: 202718819

A Tits alternative for surface group diffeomorphisms and Abelian-by-Cyclic actions on surfaces containing an Anosov diffeomorphism

@article{Hurtado2019ATA,
  title={A Tits alternative for surface group diffeomorphisms and Abelian-by-Cyclic actions on surfaces containing an Anosov diffeomorphism},
  author={Sebasti{\'a}n Hurtado and Jinxin Xue},
  journal={arXiv: Dynamical Systems},
  year={2019}
}
We obtain three main results about smooth group actions on surfaces. Our first theorem states that if a group of diffeomorphisms of a surface contains an Anosov diffeomorphism then the group contains a free subgroup or preserves one of the stable or unstable foliations up to finite index. We consider this result as a version of Tits alternative for diffeomorphism group. This theorem combined with various techniques including properties of Misiurewicz-Ziemian rotation sets, Herman-Yoccoz Theory… Expand
3 Citations

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