  We prove asymptotic stability of the Poisson homogeneous equilibrium among
solutions of the Vlassov-Poisson system in the Euclidean space $\mathbb{R}^3$.
More precisely, we show that small, smooth, and localized perturbations of the
Poisson equilibrium lead to global solutions of the Vlasov-Poisson system,
which scatter to linear solutions at a polynomial rate as $t\to\infty$.
  The Euclidean problem we consider here differs significantly from the
classical work on Landau damping in the periodic setting, in several ways. Most
importantly, the linearized problem cannot satisfy a "Penrose condition". As a
result, our system contains resonances (small divisors) and the electric field
is a superposition of an electrostatic component and a larger oscillatory
component, both with polynomially decaying rates.
