  We present a theoretical study of the static and dynamical properties of the
Kitaev magnet $\beta$-Li$_2$IrO$_3$ based on the minimal $J$-$K$-$\Gamma$
model. We argue that the incommensurate magnetic order of $\beta$-Li$_2$IrO$_3$
can be qualitatively understood in terms of a long-wavelength twisting of a
nearby commensurate, period-3 state, that shares the same symmetry, propagation
vector, counter-rotation of the two spin sublattices, and non-coplanarity. This
period-3 state shows very different structure when either the Kitaev
interaction $K$ or the off-diagonal exchange anisotropy $\Gamma$ is dominant,
featuring in particular ferromagnetic or antiferromagnetic spin dimers,
respectively. We compute the magnon excitation spectra and the dynamical spin
structure factor for both structures. The results for the momentum and energy
dependence of the neutron-scattering intensity provide distinctive qualitative
and quantitative fingerprints of the $K$-dominant or $\Gamma$-dominant states
and thus gives additional information on the relative strength of these
interactions in $\beta$-Li$_2$IrO$_3$.
