  Anisotropic spin-spin interactions of Dzyaloshinsky and Moriya symmetry are
generally considered weak, as they depend on the spin-orbit couplings. In spin
systems with gapped ground states they can, however, have rather strong
effects. We will discuss recent results related to the results of neutron
scattering and ESR for $\rm SrCu_2(BO_3)_2$. Inclusion of the
Dzyaloshinsky-Moriya interactions can explain much of the dynamics of the
systems discussed, in particular the splitting and dispersion of the triplet
modes. Some effects remain to be explained, however. Symmetries of the crystal
lead to the prediction of zero intensity for transitions, for example between
the ground state and the triplets observed in ESR.
  We present recent calculations of the effects of anisotropic terms generated
dynamically, ie linearly in the phonon coordinates. We discuss how this leads
to a novel mechanism to explain the ESR intensities. For polarized neutron
scattering experiments, we can calculate the mixing of nuclear and magnetic
scattering amplitudes by such a term and how such mixing should be observed.
