  The Ising approximation of the Heisenberg model in a strong magnetic field,
with two, three and six spin exchange interactions is studied on a kagome
chain. The kagome chain can be considered as an approximation of the third
layer of 3He absorbed on the surface of graphite (kagome lattice). By using
dynamical approach we have found one and multi-dimensional mappings (recursion
relations) for the partition function. The magnetization diagrams are plotted
and they show that the kagome chain is separating into four sublattices with
different magnetizations. Magnetization curves of two sublattices exhibit
plateaus at zero and 2/3 of the saturation field. The maximal Lyapunov exponent
for multi-dimensional mapping is considered and it is shown that near the
magnetization plateaus the maximal Lyapunov exponent also exhibits plateaus.
