Guided wave dispersion is commonly assessed by Fourier analysis of the field along a line, resulting in frequency-wave-number dispersion curves. In anisotropic plates, a point source can generate multiple dispersion branches pertaining to the same modal surface, which arise due to the angle between the power flux and the wave vector. We show that this phenomenon is very particular near zero-group-velocity points and occurs in all directions independent of the degree of anisotropy. Stationary phase points accurately describe measurements on a monocrystalline silicon plate.