The least action principle (LAP) is a dynamically rigorous method for
deriving the history of galaxy orbits. In particular it is an Omega te
st, predicting current epoch galaxy velocities as a function of positi
on and of the cosmological background. It is most usefully applied to
in-falling structures, such as the local group, where its application
indicates that the preferred cosmological model is Omega(0) = 0.1 and
h = 0.75 (h is the Hubble parameter in units of 100 km s(-1) Mpc(-1)).
The method assumes that all the mass acts as if it were distributed a
s the visible galaxies. We test the reliability of the LAP to Local Gr
oup-like systems extracted from Omega(0) = 1 n-body simulations. While
the orbits of the galaxies are qualitatively well reconstructed, the
LAP systematically underestimates the mass of the system. This failure
is attributed to the presence of extended halos weakly clustered arou
nd visible galaxies which prevent a large fraction of the group mass f
rom being detected by the LAP technique. We conclude that the LAP meth
od cannot rule out an Omega(0) = 1 value on the Local Group scale. Bet
ter constraints on Omega(0) may be obtained by applying this technique
to in-falling systems, such as clusters, containing objects with sepa
rations large compared to galaxy sizes.