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.1 Piecewise isometries are higher-dimensional generalizations of interval exchange transformations; the theory has applications in outer billiards, digital filters, and granular mixing.12
References
References
- Goetz, Arek (2003). "Piecewise Isometries — An Emerging Area of Dynamical Systems". Fractals in Graz 2001. Birkhäuser: 135–144. doi:10.1007/978-3-0348-8014-5_4.
- Smith, Lauren D.; Umbanhowar, Paul B.; Lueptow, Richard M.; Ottino, Julio M. (20 April 2019). "The geometry of cutting and shuffling: An outline of possibilities for piecewise isometries". Physics Reports. 802: 1–22. doi:10.1016/j.physrep.2019.01.003. ISSN 0370-1573.
Further reading
Further reading
- Goetz, Arek (1 September 2000). "Dynamics of piecewise isometries". Illinois Journal of Mathematics. 44 (3). doi:10.1215/ijm/1256060408.
- Buzzi, Jérôme (October 2001). "Piecewise isometries have zero topological entropy". Ergodic Theory and Dynamical Systems. 21 (5): 1371–1377. doi:10.1017/S0143385701001651. ISSN 1469-4417.
- Bressaud, Xavier; Poggiaspalla, Guillaume (January 2007). "A Tentative Classification of Bijective Polygonal Piecewise Isometries". Experimental Mathematics. 16 (1): 77–99. doi:10.1080/10586458.2007.10128987.
- Peres, Pedro; Rodrigues, Ana (2019). "Dynamics of Planar Piecewise Isometries: Recent Advances". Boletim da Sociedade Portuguesa de Matemática (in Portuguese). 77: 105–118. ISSN 0872-3672.