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

Magnetization and Lyapunov exponents on a kagome chain with multi-site exchange interaction