  We consider the steady Swift - Hohenberg partial differential equation. It is
a one-parameter family of PDE on the plane, modeling for example Rayleigh -
B\'enard convection. For values of the parameter near its critical value, we
look for small solutions, quasiperiodic in all directions of the plane and
which are invariant under rotations of angle \pi/q, q\geq 4. We solve an
unusual small divisor problem, and prove the existence of solutions for small
parameter values.
