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Forced Symmetry Breaking and Relative Periodic Orbits

In: Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

Author

Listed:
  • Frédéric Guyard

    (École Polytechnique Fédéral de Lausanne, DMA)

  • Reiner Lauterbach

    (Universität Hamburg, Fachbereich Mathematik)

Abstract

We would like to discuss some aspects of forced symmetry breaking in equivariant systems. This topic is of significance for applications since in real life systems symmetries occur only as approximations. This is in particular relevant for the applications of genericity theories. There are certain dynamical features (heteroclinic cycles) which are generic within the class of symmetric systems, however they are of high codimension in the context of general dynamical systems. Therefore one might expect that forced symmetry breaking destroys such behavior. However it has been observed that weak perturbations of symmetric systems can introduce new complicated dynamical properties. Therefore it is interesting to study the influence of weak symmetry breaking from a purely mathematical point of view as well as from an applied point of view. In this paper we focus on the mathematical part and we try to describe some of our ideas in geometrical terms.

Suggested Citation

  • Frédéric Guyard & Reiner Lauterbach, 2001. "Forced Symmetry Breaking and Relative Periodic Orbits," Springer Books, in: Bernold Fiedler (ed.), Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, pages 453-468, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56589-2_20
    DOI: 10.1007/978-3-642-56589-2_20
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