  Using a nominally symmetric annular combustor, we present experimental
evidence of a predicted spontaneous symmetry breaking and an unexpected
explicit symmetry breaking in the neighborhood of the Hopf bifurcation, which
separates linearly-stable azimuthal thermoacoustic modes from self-oscillating
modes. We derive and solve a multidimensional Fokker-Planck equation to unravel
a unified picture of the phase space topology. We demonstrate that symmetric
probability density functions of the thermoacoustic state vector are elusive,
because the effect of asymmetries, even imperceptible ones, is magnified close
to the bifurcation.
