  We explore in detail the dynamics of multi-field inflationary models. We
first revisit the two-field case and rederive the coordinate independent
expression for the attractor solution with either small or large turn rate,
emphasizing the role of isometries for the existence of rapid-turn solutions.
Then, for three fields in the slow-twist regime we provide elegant expressions
for the attractor solution for generic field-space geometries and potentials
and study the behaviour of first order perturbations. For generic
$\mathcal{N}$-field models, our method quickly grows in algebraic complexity.
We observe that field-space isometries are common in the literature and are
able to obtain the attractor solutions and deduce stability for some isometry
classes of $\mathcal{N}$-field models. Finally, we apply our discussion to
concrete supergravity models. These analyses conclusively demonstrate the
existence of $\mathcal{N}>2$ dynamical attractors distinct from the two-field
case, and provide tools useful for future studies of their phenomenology in the
cosmic microwave background and stochastic gravitational wave spectrum.
