We perform a detailed numerical analysis of inflationary solutions in Kahler
moduli of type IIB flux compactifications. We show that there are inflationary
solutions even when all the fields play an important role in the overall shape
of the scalar potential. Moreover, there exists a direction of attraction for
the inflationary trajectories that correspond to the constant volume direction.
This basin of attraction enables the system to have an island of stability in
the set of initial conditions. We provide explicit examples of these
trajectories, compute the corresponding tilt of the density perturbations power
spectrum and show that they provide a robust prediction of n_s approximately
0.96 for 60 e-folds of inflation.Comment: 27 pages, 9 figure