PIECEWISE CONTRACTIONS ARE ASYMPTOTICALLY PERIODIC

@inproceedings{Deane2008PIECEWISECA,
  title={PIECEWISE CONTRACTIONS ARE ASYMPTOTICALLY PERIODIC},
  author={Jonathan H. B. Deane},
  year={2008}
}
We show that, given a finite partition of the plane C such that the map G acts as a linear contraction on each part, for almost every choice of parameters every orbit of G is (asymptotically) periodic. 
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