  We find an exact solution of the equations of motion of a two-field
cosmological model, which realizes multi-field dark energy. The latter is
characterized by field-space trajectories with turning rates that are always
large. We study a class of two-field models and show that it is possible to
have such trajectories, giving accelerated space-time expansion, even when the
scalar potential preserves the rotational invariance of the field-space metric.
For the case of Poincar\'e-disk field space, we derive the form of the scalar
potential compatible with such background solutions and, furthermore, we find
the exact solutions analytically. Their field-space trajectories are spirals
inward, toward the center of the Poincar\'e disk. Interestingly, the functional
form of the relevant scalar potential is compatible with a certain hidden
symmetry, although the latter is broken by the presence of a constant term.
