  We show an abstract time-periodic bifurcation theorem in Banach spaces. The
key point as well as the novelty of the method is to split the original
evolution equation into two different coupled equations, one for the
time-average of the sought solution and the other for the "purely periodic"
component. This approach may be particularly useful in studying physical
phenomena occurring in unbounded spatial regions. Actually, we furnish a
significant application of the theorem, by providing sufficient conditions for
time-periodic bifurcation from a steady-state flow of a Navier-Stokes liquid
past a three-dimensional obstacle.
