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Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems pp 649–689Cite as

The Orbit Space Method: Theory and Application

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Abstract

If a system does not change its structure, while it is exposed to some transformations such as translations, rotations, reflections, or even more complicated transformations, it possesses symmetry. This is a feature of a host of phenomena. A good mathematical description of them must take the symmetry into account. Further symmetry may come about by simplifications. Often, deep statements are possible just by symmetry arguments. On the other hand, the presence of symmetry helps to analyze a given system. For example, one can find new solutions knowing a special one. Or, the symmetry may exclude some situations or force some phenomena to appear, which usually do not occur in generic nonsymmetrical systems.

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Author information

Authors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, 80290, München, Germany

    Matthias Rumberger & Jürgen Scheurle

Authors
  1. Matthias Rumberger
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  2. Jürgen Scheurle
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Editor information

Editors and Affiliations

  1. Freie Universität Berlin Institut für Mathematik I, Arnimallee 2-6, 14195, Berlin, Germany

    Bernold Fiedler

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© 2001 Springer-Verlag Berlin Heidelberg

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Rumberger, M., Scheurle, J. (2001). The Orbit Space Method: Theory and Application. In: Fiedler, B. (eds) Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56589-2_27

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  • DOI: https://doi.org/10.1007/978-3-642-56589-2_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-62524-4

  • Online ISBN: 978-3-642-56589-2

  • eBook Packages: Springer Book Archive

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