  Motivated by recent interest in the role of the hyperfine interaction in
quantum dots we study the dynamics of a localized electron spin coupled to many
nuclei. An important feature of the model is that the coupling to an individual
nuclear spin depends on its position in the quantum dot. We introduce a
semi-classical description of the system valid in the limit of a large number
of nuclei and analyze the resulting classical dynamics. Contrary to a natural
assumption, the correlation functions of electron spin with an arbitrary
initial condition show no decay in time. Rather, they exhibit complicated
undamped oscillations. This may be attributed to the fact that the system has
many integrals of motion and is close to an integrable one. The ensemble
averaged correlation functions do exhibit a slow decay (1/ln(t)) for t ->
\infty.
