  We use sample of 813 Lyman-break galaxies (LBGs) with 2.6<z<3.4 to perform a
detailed analysis of the redshift-space (z-space) distortions in their
clustering pattern and from them derive confidence levels in the
[Omega_m,beta(z=3)] plane. We model the z-space distortions in the shape of the
correlation function measured in orthogonal directions, xi(sigma,pi). This
modeling requires an accurate description of the real-space correlation
function to be given as an input. From the projection of xi(sigma,pi) in the
angular direction, w_p(sigma), we derive the best fitting amplitude and slope
for the LBG real-space correlation function: r_0=4.48(+0.17)(-0.18) h(-1) Mpc
and gamma=1.76(+0.08)(-0.09) (xi(r)= (r/r_0)^-gamma). A comparison between the
shape of xi(s) and w_p(sigma) suggests that xi(r) deviates from a simple
power-law model, with a break at ~9 h(-1) Mpc. This model is consistent with
the observed projected correlation function. However, due to the limited size
of the fields used, the w_p(sigma) results are limited to sigma < 10 h(-1) Mpc.
Assuming this double power-law model, and by analysing the shape distortions in
xi(sigma,pi), we find the following constraints: beta(z=3) = 0.15
(+0.20)(-0.15), Omega_m = 0.35 (+0.65)(-0.22). Combining these results with
orthogonal constraints from linear evolution of density perturbations, we find
that beta(z=3) = 0.25 (+0.05)(-0.06), Omega_m = 0.55 (+0.45)(-0.16).
