  Using Monte Carlo and spin-dynamics methods, we have investigated the dynamic
behavior of the classical, antiferromagnetic XY model on a triangular lattice
with linear sizes $L \leq 300$. The temporal evolutions of spin configurations
were obtained by solving numerically the coupled equations of motion for each
spin using fourth-order Suzuki-Trotter decompositions of exponential operators.
  From space- and time-displaced spin-spin correlation functions and their
space-time Fourier transforms we obtained the dynamic structure factor $S({\bf
q},w)$ for momentum ${\bf q}$ and frequency $\omega$. Below
$T_{KT}$(Kosterlitz-Thouless transition), both the in-plane ($S^{xx}$) and the
out-of-plane ($S^{zz}$) components of $S({\bf q},\omega)$ exhibit very strong
and sharp spin-wave peaks. Well above $T_{KT}$, $S^{xx}$ and $S^{zz}$
apparently display a central peak, and spin-wave signatures are still seen in
$S^{zz}$. In addition, we also observed an almost dispersionless domain-wall
peak at high $\omega$ below $T_{c}$(Ising transition), where long-range order
appears in the staggered chirality. Above $T_{c}$, the domain-wall peak
disappears for all $q$. The lineshape of these peaks is captured reasonably
well by a Lorentzian form. Using a dynamic finite-size scaling theory, we
determined the dynamic critical exponent $z$ = 1.002(3). We found that our
results demonstrate the consistency of the dynamic finite-size scaling theory
for the characteristic frequeny $\omega_{m}$ and the dynamic structure factor
$S({\bf q},\omega)$ itself.
