  Evidences are presented concerning tantalizing regularities in cities'
population-flows in what regards to space and time correlations. The former
exhibit a distance-behavior (for large distances) compatible with the inverse
square law, following an overall Lorentzian dependence with an scale-parameter
of $74\pm6$ km. The later decay exponentially with a characteristic time of
$17.2\pm1.3$ years. These features can be explained by a dynamical model for
cities' population-growth of a Lagevinian nature. Numerical simulations based
on the model confirm its applicability. The model also allows for the
identification of collective normal modes of city-growth dynamics that can be
empirically identified.
