Now showing items 1-3 of 3

  • Cone exchange transformations and boundedness of orbits 

    Ashwin, Peter; Goetz, Arek (Cambridge University Press, 2010)
    We introduce a class of two-dimensional piecewise isometries on the plane that we refer to as cone exchange transformations (CETs). These are generalizations of interval exchange transformations (IETs) to 2D unbounded ...
  • Invariant curves and explosion of periodic Islands in systems of piecewise rotations 

    Ashwin, Peter; Goetz, Arek (Society for Industrial and Applied Mathematics, 2005)
    Invertible piecewise isometric maps (PWIs) of the plane, in spite of their apparent simplicity, can show a remarkable number of dynamical features analogous to those found in nonlinear smooth area preserving maps. There ...
  • Polygonal invariant curves for a planar piecewise isometry 

    Ashwin, Peter; Goetz, Arek (American Mathematical Society, 2005)
    We investigate a remarkable new planar piecewise isometry whose generating map is a permutation of four cones. For this system we prove the coexistence of an infinite number of periodic components and an uncountable number ...