Hidden Symmetry and Genericity

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.