Browsing Mathematics by Author "Goetz, Arek"
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Cone exchange transformations and boundedness of orbits
Ashwin, Peter; Goetz, Arek (Cambridge University Press, 2010)We introduce a class of twodimensional 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 ...