Abstract
We present several examples of piecewise isometric systems that give rise to complex structures of their coding partitions. We also list and comment on current open questions in the area that pertain to fractal-like structure of cells. Piecewise isometries are two and higher dimensional generalizations of interval exchanges and interval translations. The interest in the dynamical systems of piecewise isometries is partially catalyzed by potential applications and the fact that simple geometric constructions give rise to rich phenomena and amazing fractal graphics. Piecewise isometric systems appear in dual billiards, Hamiltonian systems, and digital filters.
Published Version
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