Bifurcation structure of the C-type period-doubling transition

► Unusual bifurcation phenomena in forced period-doubling oscillators. ► Formation of multi-layered resonance tori through transverse period doubling. ► Transitions from multi-layered resonance torus to period-doubled ergodic torus. ► Formation of pairs of period-doubled ergodic tori through torus-fold bifurcation. ► Global bifurcation between unstable period-2 torus and stable two-band torus.