  NoAM for "No Action Method" is a framework for reconstructing the past orbits
of observed tracers of the large scale mass density field. It seeks exact
solutions of the equations of motion (EoM), satisfying initial homogeneity and
the final observed particle (tracer) positions. The solutions are found
iteratively reaching a specified tolerance defined as the RMS of the distance
between reconstructed and observed positions. Starting from a guess for the
initial conditions, NoAM advances particles using standard N-body techniques
for solving the EoM. Alternatively, the EoM can be replaced by any
approximation such as Zel'dovich and second order perturbation theory (2LPT).
NoAM is suitable for billions of particles and can easily handle non-regular
volumes, redshift space, and other constraints. We implement NoAM to
systematically compare Zel'dovich, 2LPT, and N-body dynamics over diverse
configurations ranging from idealized high-res periodic simulation box to
realistic galaxy mocks. Our findings are (i) Non-linear reconstructions with
Zel'dovich, 2LPT, and full dynamics perform better than linear theory only for
idealized catalogs in real space. For realistic catalogs, linear theory is the
optimal choice for reconstructing velocity fields smoothed on scales > 5 Mpc/h.
(ii) all non-linear back-in-time reconstructions tested here, produce
comparable enhancement of the baryonic oscillation signal in the correlation
function.
