  We investigate statistically the dynamical consequences of cosmological
fluxes of matter and related moments on progenitors of today's dark matter
haloes. Their dynamics is described via canonical perturbation theory which
accounts for two types of perturbations: the tidal field corresponding to
fly-bys and accretion of dark matter through the halo's outer boundary. he
dynamical equations are solved linearly, order by order, projecting on a
biorthogonal basis to consistently satisfy the field equation. Since our
solution of the Boltzmann Poisson equations is explicit, it allows statistical
predictions for the ensemble distribution of the inner dynamical features of
haloes. The secular evolution of open galactic haloes is investigated: we
derive the kinetic equation which governs the quasi-linear evolution of dark
matter profile induced by infall and its corresponding gravitational
correlations. This yields a Fokker Planck-like equation for the angle-averaged
underlying distribution function. We show how these extensions to the classical
theory could be used to (i) observationally constrain the statistical nature of
the infall (ii) predict the observed distribution and correlations of
substructures in upcoming surveys, (iii) predict the past evolution of the
observed distribution of clumps, and finally (iv) weight the relative
importance of the intrinsic (via the unperturbed distribution function) and
external (tidal and/ or infall) influence of the environment in determining the
fate of galaxies.
