Groups of piecewise linear homeomorphisms of flows

@article{MatteBon2018GroupsOP,
  title={Groups of piecewise linear homeomorphisms of flows},
  author={Nicol{\'a}s Matte Bon and Michele Triestino},
  journal={Compositio Mathematica},
  year={2018},
  volume={156},
  pages={1595 - 1622}
}
To every dynamical system $(X,\varphi )$ over a totally disconnected compact space, we associate a left-orderable group $T(\varphi )$. It is defined as a group of homeomorphisms of the suspension of $(X,\varphi )$ which preserve every orbit of the suspension flow and act by dyadic piecewise linear homeomorphisms in the flow direction. We show that if the system is minimal, the group is simple and, if it is a subshift, then the group is finitely generated. The proofs of these two statements are… 
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