  A spin wave theory explaining experimentally observed frequency splitting of
dynamical excitations with azimuthal symmetry of a magnetic dot in a vortex
ground state is developed. It is shown that this splitting is a result of the
dipolar hybridization of three spin wave modes of a dot having azimuthal
indices |m|=1: two high-frequency azimuthal excitation modes of the in-plane
part of the vortex with indices m = +/-1 and a low-frequency m= +1 gyrotropic
mode describing the translational motion of the vortex core. The analytically
calculated magnitude of the frequency splitting is proportional to the ratio of
the dot thickness to its radius and quantitatively agrees with the results of
time resolved Kerr experiments.
