  We make the first steps towards an understanding of the ergodic properties of
a rational map defined over a complete algebraically closed non-archimedean
field. For such a rational map R, we construct a natural invariant probability
measure m_R which reprensents the asymptotic distribution of preimages of
non-exceptional point. We show that this measure is exponentially mixing, and
satisfies the central limit theorem. We prove some general bounds on the metric
entropy of m_R, and on the topological entropy of R. We finally prove that
rational maps with vanishing topological entropy have potential good reduction.
