  A real-space renormalization transformation is constructed for lattices of
non-identical oscillators with dynamics of the general form
$d\phi_{k}/dt=\omega_{k}+g\sum_{l}f_{lk}(\phi_{l},\phi_{k})$. The
transformation acts on ensembles of such lattices. Critical properties
corresponding to a second order phase transition towards macroscopic
synchronization are deduced. The analysis is potentially exact, but relies in
part on unproven assumptions. Numerically, second order phase transitions with
the predicted properties are observed as $g$ increases in two structurally
different, two-dimensional oscillator models. One model has smooth coupling
$f_{lk}(\phi_{l},\phi_{k})=\phi(\phi_{l}-\phi_{k})$, where $\phi(x)$ is
non-odd. The other model is pulse-coupled, with
$f_{lk}(\phi_{l},\phi_{k})=\delta(\phi_{l})\phi(\phi_{k})$. Lower bounds for
the critical dimensions for different types of coupling are obtained. For
non-odd coupling, macroscopic synchronization cannot be ruled out for any
dimension $D\geq 1$, whereas in the case of odd coupling, the well-known result
that it can be ruled out for $D< 3$ is regained.
