Piecewise isometry

In mathematics, a piecewise isometry is a dynamical system that consists of finitely many Euclidean isometries acting in different places, including rotations, translations, and reflections. Piecewise isometries are higher-dimensional generalizations of interval exchange transformations; the theory has applications in outer billiards, digital filters, and granular mixing.

References

  1. 1 2 Goetz, Arek (2003). "Piecewise Isometries — an Emerging Area of Dynamical Systems". Fractals in Graz 2001. pp. 135–144. doi:10.1007/978-3-0348-8014-5_4. ISBN 978-3-0348-9403-6.
  2. ↑ Smith, Lauren D.; Umbanhowar, Paul B.; Lueptow, Richard M.; Ottino, Julio M. (2019). "The geometry of cutting and shuffling: An outline of possibilities for piecewise isometries". Physics Reports. 802: 1–22. Bibcode:2019PhR...802....1S. doi:10.1016/j.physrep.2019.01.003.

Further reading