  We derive the formula of the complex Doppler shift in a two-dimensional,
dispersive metamaterial and we show that a moving, monochromatic radiation
source generates multiple frequency modes. The role of the group velocity is
stressed and the Doppler shifted radiation field exhibits features of the
Cherenkov effect. The presented theory is also applicable to the case of a
moving, nonoscillating charge and explains many peculiar characteristics of the
Cherenkov radiation in lefthanded metamaterials such as the backward direction
of power emission, the constant radiation angle and the lack of velocity
threshold.
