  Consider a time-dependent Hamiltonian $H(Q,P;x(t))$ with periodic driving
$x(t)=A\sin(\Omega t)$. It is assumed that the classical dynamics is chaotic,
and that its power-spectrum extends over some frequency range
$|\omega|<\omega_{cl}$. Both classical and quantum-mechanical (QM) linear
response theory (LRT) predict a relatively large response for
$\Omega<\omega_{cl}$, and a relatively small response otherwise, independently
of the driving amplitude $A$. We define a non-perturbative regime in the
$(\Omega,A)$ space, where LRT fails, and demonstrate this failure numerically.
For $A>A_{prt}$, where $A_{prt}\propto\hbar$, the system may have a relatively
strong response for $\Omega>\omega_{cl}$, and the shape of the response
function becomes $A$ dependent.
