The Orbit Space Method: Theory and Application

Matthias Rumberger () and Jürgen Scheurle ()
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Matthias Rumberger: Technische Universität München, Zentrum Mathematik
Jürgen Scheurle: Technische Universität München, Zentrum Mathematik

A chapter in Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, 2001, pp 649-689 from Springer

Abstract: 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.

Keywords: Vector Field; Lyapunov Exponent; Tangent Space; Periodic Point; Relative Equilibrium (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-3-642-56589-2_27

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