Pitchfork and transcritical bifurcations in systems with homogeneous nonlinearities and an almost periodic time coefficient

The zero solution of a vector valued differential equation with an autonomous linear part and a homogeneous nonlinearity multiplied by an almost periodic function is shown to undergo pitchfork or transcritical bifurcations to small nontrivial almost periodic soutions as a leading simple real eigenvalue of the linear part crosses the imaginary axis.