Chaotic planar states of the discrete dynamical anisotropic Heisenberg spin chain

Planar states of the semi-infinite classical, discrete dynamical anisotropic Heisenberg spin chain are shown to be completely chaotic in the sense that for any degree of anisotropy the states are totally aperiodic for almost all values of the first spin S1 in the chain, while on a dense set of S1 one obtains, with minor exceptions, periodic states of all orders exceeding a certain number which depends on the degree of anisotropy. Such states are not present in the isotropic chain.