  We show that a special type of orbits, which are non-periodic and complex,
'Saddle Orbits' (SOs) describe accurately the quantal and experimental current
oscillations in the Resonant Tunneling Diode in tilted fields. This is the
first demonstration that one needs to abandon the periodic orbits (POs)
paradigm in favour of this new and peculiar type of orbit. The SOs solve the
puzzle of broad regions of experimental oscillations where we find no real or
complex PO that can explain the data. The SOs succeeds in regimes involving
several non-isolated POs, where PO formulas fail.
