  We define center manifold as usual as an invariant manifold, tangent to the
invariant subspace of the linearization of the mapping defining a continuous
dynamical system, but the center subspace that we consider is associated with
eigenvalues with small but not necessarily zero} real parts. We prove existence
and smoothness of such center manifold assuming that certain inequalities
between the center eigenvalues and the rest of the spectrum hold. The theorem
is valid for finite-dimensional systems, as well as for infinite-dimensional
systems provided they satisfy an additional condition. We show that the
condition holds for the Navier-Stokes equation subject to appropriate boundary
conditions.
