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
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.