  We study mappings obtained as s-periodic reductions of the lattice
Korteweg-De Vries equation. For small s=(s1,s2) we establish upper bounds on
the growth of the degree of the numerator of their iterates. These upper bounds
appear to be exact. Moreover, we conjecture that for any s1,s2 that are
co-prime the growth is ~n^2/(2s1s2), except when s1+s2=4 where the growth is
linear ~n. Also, we conjecture the degree of the n-th iterate in projective
space to be ~n^2(s1+s2)/(2s1s2).
