Topological singularities and phonon focusing

The focusing directions of phonon images generated by the anisotropic propagation of ballistic phonons are interpreted as singularities of the Gauss map of the energy surface. While a linear dispersion produces only folds and cusps, a nonlinear dispersion relation generically induces singular events for critical values of the frequency. These events are classified by means of catastrophe theory and the local topology on the energy surfaces is elucidated. On reflection planes or symmetry axes new types of singularities occur. The consequences of Morse singularities in the dispersion relation for the focusing directions are discussed.