  In this manuscript, we investigate the oscillatory behaviour of the
anisotropy in the diagonal Bianchi-I spacetimes. Our starting point is a
simplification of Einstein's equations using only observable or physical
variables. As a consequence, we are able to: (a) Prove general results
concerning the existence of oscillations of the anisotropy in the primordial
and the late-time universe. For instance, in the expanding scenario, we show
that a past weakly mixmaster behaviour (oscillations as we approach the Kasner
solutions) might appear even with no violation of the usual energy conditions,
while in the future, the pulsation (oscillations around isotropic solutions)
seems to be most favored; (b) Determine a large scheme for deriving classes of
physically motivated exact solutions, and we give some (including the general
barotropic perfect fluid and the magnetic one); (c) Understand the physical
conditions for the occurrence of the isotropization or anisotropization during
the cosmological evolution; (d) Understand how anisotropy and energy density
are converted one into another. In particular, we call attention to the
presence of a residue in the energy density in a late-time isotropic universe
coming from its past anisotropic behaviour.
