  Nonlinear resonances in the classical phase space lead to a significant
enhancement of tunneling. We demonstrate that the double resonance gives rise
to a complicated tunneling peak structure. Such double resonances occur in
Hamiltonian systems with an at least four-dimensional phase space. To explain
the tunneling peak structure, we use the universal description of single and
double resonances by 4D normal-form Hamiltonians. By applying perturbative
methods, we reveal the underlying mechanism of enhancement and suppression of
tunneling and obtain excellent quantitative agreement. Using a minimal matrix,
we obtain model an intuitive understanding.
