Piecewise isometry
From HandWiki
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.[1][2]
References
- ↑ 1.0 1.1 Goetz, Arek (2003). "Piecewise Isometries — An Emerging Area of Dynamical Systems" (in en). Fractals in Graz 2001 (Birkhäuser): 135–144. doi:10.1007/978-3-0348-8014-5_4. https://link.springer.com/chapter/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. https://www.sciencedirect.com/science/article/pii/S0370157319300031.
Further reading
- Goetz, Arek (1 September 2000). "Dynamics of piecewise isometries". Illinois Journal of Mathematics 44 (3). doi:10.1215/ijm/1256060408. https://projecteuclid.org/journals/illinois-journal-of-mathematics/volume-44/issue-3/Dynamics-of-piecewise-isometries/10.1215/ijm/1256060408.full.
- Buzzi, Jérôme (October 2001). "Piecewise isometries have zero topological entropy" (in en). Ergodic Theory and Dynamical Systems 21 (5): 1371–1377. doi:10.1017/S0143385701001651. ISSN 1469-4417. https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/abs/piecewise-isometries-have-zero-topological-entropy/5A7DEB99DE824E62AB991A252B0156EC.
- 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. https://www.tandfonline.com/doi/abs/10.1080/10586458.2007.10128987.
- Peres, Pedro; Rodrigues, Ana (2019). "Dynamics of Planar Piecewise Isometries: Recent Advances" (in pt). Boletim da Sociedade Portuguesa de Matemática 77: 105–118. ISSN 0872-3672. https://revistas.rcaap.pt/boletimspm/article/view/21035.
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