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Piecewise Isometries — An Emerging Area of Dynamical Systems

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Fractals in Graz 2001

Part of the book series: Trends in Mathematics ((TM))

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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA, 94703, USA

    Arek Goetz

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  1. Arek Goetz
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Editors and Affiliations

  1. Institut für Mathematik A, Technische Universität Graz, Steyrergasse 30, 8010, Graz, Austria

    Peter Grabner

  2. Institut für Mathematik C, Technische Universität Graz, Steyrergasse 30, 8010, Graz, Austria

    Wolfgang Woess

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© 2003 Springer Basel AG

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Goetz, A. (2003). Piecewise Isometries — An Emerging Area of Dynamical Systems. In: Grabner, P., Woess, W. (eds) Fractals in Graz 2001. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8014-5_4

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  • DOI: https://doi.org/10.1007/978-3-0348-8014-5_4

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9403-6

  • Online ISBN: 978-3-0348-8014-5

  • eBook Packages: Springer Book Archive

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