  Dynamic mean field theory is applied to the problem of forest fires. The
starting point is the Monte Carlo simulation in a lattice of million cells. The
statistics of the clusters is obtained by means of the Hoshen--Kopelman
algorithm. We get the map $p_n\to p_{n+1}$, where $p_n$ is the probability of
finding a tree in a cell, and $n$ is the discrete time. We demonstrate that the
time evolution of $p$ is chaotic. The arguments are provided by the calculation
of the bifurcation diagram and the Lyapunov exponent. The bifurcation diagram
reveals several windows of stability, including periodic orbits of length
three, five and seven. For smaller lattices, the results of the iteration are
in qualitative agreement with the statistics of the forest fires in Canada in
years 1970--2000.
