  The global attraction is proved for the nonlinear 3D Klein-Gordon equation
with a nonlinearity concentrated at one point. Our main result is the
convergence of each "finite energy solution" to the manifold of all solitary
waves as $t\to\pm\infty$. This global attraction is caused by the nonlinear
energy transfer from lower harmonics to the continuous spectrum and subsequent
dispersion radiation.
  We justify this mechanism by the following strategy based on inflation of
spectrum by the nonlinearity. We show that any omega-limit trajectory has the
time-spectrum in the spectral gap $[-m,m]$ and satisfies the original equation.
Then the application of the Titchmarsh Convolution Theorem reduces the spectrum
of each omega-limit trajectory to a single frequency $\omega\in[-m,m]$.
