2 documents found, page 1 of 1
Renormalization of translated cone exchange transformations
Cockram, Noah; Ashwin, Peter; Rodrigues, AnaIn this paper, we investigate a class of non-invertible piecewise isometries on the upper half-plane known as Translated Cone Exchanges. These maps include a simple interval exchange on a boundary we call the baseline. We provide a geometric construction for the first return map to a neighbourhood of the vertex of the middle cone for a large class of parameters, then we show a recurrence in the first return map...
Construction of invariant curves for some piecewise isometries
Rodrigues, Ana; Ashwin, Peter; Cokram, NoahWe establish conditions for the existence of a family of piecewise linear invariant curves in a two-parameter family of piecewise isometries on the upper half-plane known as Translated Cone Exchange Transformations. We show that these curves are embeddings of interval exchange transformations and give rise to layers of invariant regions. We also show the existence of a trapezoidal piecewise isometry for which t...