  Multi-field inflation with a curved scalar geometry has been found to support
background trajectories that violate the slow-roll, slow-turn conditions and
thus have the potential to evade the swampland constraints. In order to
understand how generic this novel behaviour is and what conditions lead to it,
we perform a classification of dynamical attractors of two-field inflation that
are of the scaling type. Scaling solutions form a one-parameter generalization
of De Sitter solutions with a constant value of the first Hubble flow parameter
$\epsilon$ and, as we argue and demonstrate, form a natural starting point for
the study of non-slow-roll slow-turn behaviour.
  All scaling solutions can be classified as critical points of a specific
dynamical system. We recover known multi-field inflationary attractors as
approximate scaling solutions and classify their stability using dynamical
system techniques. In particular, we discover that dynamical bifurcations play
an integral role in the transition between geodesic and non-geodesic motion and
discuss the ability of scaling solutions to describe realistic multi-field
models. We revisit the criteria for background stability and show cases where
the usual criteria found in the literature do not capture the background
evolution of the system.
