  The effective potential neighboring the corotation resonance region in barred
galaxies is shown to be strongly time-dependent in any rotating frame because
of the competition of nearby perturbations of similar strengths with differing
rotation speeds. Contrary to the generally adopted assumption, that in the bar
rotating frame the corotation region should possess four stationary equilibrium
points (Lagrange points), with high quality N-body simulations we localize the
instantaneous equilibrium points and find that they circulate or oscillate
broadly in azimuth with respect to the pattern speeds of the inner or outer
perturbations. This implies that at the particle level the Jacobi integral is
not well conserved around the corotation radius. That is, angular momentum
exchanges decouple from energy exchanges, enhancing the chaotic diffusion of
stars through the corotation region.
