  We determine the dynamical attractors associated with anisotropic
hydrodynamics (aHydro) and the DNMR equations for a 0+1d conformal system using
kinetic theory in the relaxation time approximation. We compare our results to
the non-equilibrium attractor obtained from exact solution of the 0+1d
conformal Boltzmann equation, Navier-Stokes theory, and second-order
Mueller-Israel-Stewart theory. We demonstrate that the aHydro attractor
equation resums an infinite number of terms in the inverse Reynolds number. The
resulting resummed aHydro attractor possesses a positive longitudinal to
transverse pressure ratio and is virtually indistinguishable from the exact
attractor. This suggests that kinetic theory involves not only a resummation in
gradients (Knudsen number) but also a novel resummation in inverse Reynolds
number. We also demonstrate that the DNMR result provides a better
approximation to the exact kinetic theory attractor than Mueller-Israel-Stewart
theory. Finally, we introduce a new method for obtaining approximate aHydro
equations which relies solely on an expansion in inverse Reynolds number, carry
out this expansion to third order, and compare these third-order results to the
exact kinetic theory solution.
