Heteroclinic Cycles

Abstract

One of the classic pattern-forming systems of mathematical physics is the Rayleigh-Bénard experiment, in which a thin layer of fluid is heated from below. We discussed this experiment in Section 5.7 from the point of view of lattice-symmetric solutions to Euclidean-equivariant PDEs. In the classic experiment, the homogeneous conduction state becomes unstable and there is a bifurcation to a patterned state — typically rolls, although, as Bénard famously observed, hexagons can also occur.