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Hidden Symmetry and Genericity

  • Martin Golubitsky
  • Ian Stewart
Chapter
  • 690 Downloads
Part of the Progress in Mathematics book series (PM, volume 200)

Abstract

In Chapter 6 we discussed ways in which symmetries can be modeling assumptions in physical systems, and we framed this discussion specifically in terms of models of the Couette-Taylor experiment and the Belousov-Zhabotinskii experiment. We saw that symmetries may be exact, at least for modeling purposes, or they may be approximate. In models of the Couette-Taylor experiment, approximate symmetries appear because we assume periodic boundary conditions in the axial direction; in models of the Belousov-Zhabotinskii experiment they appear because we assume an infinitely large domain. We saw that model-independent results — those that depend only on the symmetries of the model — tell us a great deal about transitions that are actually seen in experiments.

Keywords

Mode Interaction Isotropy Subgroup Pitchfork Bifurcation Hide Symmetry Taylor Vortex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • Martin Golubitsky
    • 1
  • Ian Stewart
    • 2
  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK

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