  Dynamical tunnelling between symmetry-related stable modes is studied in the
periodically driven pendulum. We present strong evidence that the tunnelling
process is governed by nonlinear resonances that manifest within the regular
phase-space islands on which the stable modes are localized. By means of a
quantitative numerical study of the corresponding Floquet problem, we identify
the trace of such resonances not only in the level splittings between
near-degenerate quantum states, where they lead to prominent plateau
structures, but also in overlap matrix elements of the Floquet eigenstates,
which reveal characteristic sequences of avoided crossings in the Floquet
spectrum. The semiclassical theory of resonance-assisted tunnelling yields good
overall agreement with the quantum-tunnelling rates, and indicates that partial
barriers within the chaos might play a prominent role.
