  We introduce the notion of equilibrium index for statically isolated
invariant sets of the system $u_t+A u=f_\lambda(u)$ on Banach space $X$ (where
$A$ is a sectorial operator with compact resolvent) and present a reduction
theorem and an index formula for bifurcating invariant sets near equilibrium
points. Then we prove a new global static bifurcation theorem where the
crossing number $\mathfrak{m}$ may be even. In particular, in case
$\mathfrak{m}=2$, we show that the system undergoes either an
attractor/repeller bifurcation, or a global static bifurcation. An illustrating
example is also given by considering the bifurcations of the periodic boundary
value problem of second-order differential equations.
