Dilation surfaces and their Veech groups

@article{Duryev2019DilationSA,
  title={Dilation surfaces and their Veech groups},
  author={Eduard Duryev and Charles Fougeron and Selim Ghazouani},
  journal={Journal of Modern Dynamics},
  year={2019}
}
We introduce a class of objects which we call 'dilation surfaces'. These provide families of foliations on surfaces whose dynamics we are interested in. We present and analyze a couple of examples, and we define concepts related to these in order to motivate several questions and open problems. In particular we generalize the notion of Veech group to dilation surfaces, and we prove a structure result about these Veech groups. 

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