We show that special types of orbits, which are nonperiodic and complex “saddle orbits” (SOs), describe accurately the quantal and experimental current oscillations in the resonant tunneling diode in tilted fields. The SOs solve the puzzle of broad regions of experimental oscillations where we find no real or complex periodic orbit (PO) that can explain the data. The SOs succeed in regimes involving several nonisolated POs, where PO formulas fail. We show that their contribution can, unexpectedly, decay very slowly in the classical limit
