Hydrodynamic attractors in phase space

Hydrodynamic attractors have recently gained prominence in the context of early stages of ultra-relativistic heavy-ion collisions at the RHIC and LHC. We critically examine the existing ideas on this subject from a phase space point of view. In this picture the hydrodynamic attractor can be seen as a special case of the more general phenomenon of dynamical dimensionality reduction of phase space regions. We quantify this using Principal Component Analysis. Furthermore, we adapt the well known slow-roll approximation to this setting. These techniques generalize easily to higher dimensional phase spaces, which we illustrate by a preliminary analysis of a dataset describing the evolution of a 5-dimensional manifold of initial conditions immersed in a 16-dimensional representation of the phase space of the Boltzmann kinetic equation in the relaxation time approximation.