  We prove that exists a Lindstedt series that holds when a Hamiltonian is
driven by a perturbation going to infinity. This series appears to be dual to a
standard Lindstedt series as it can be obtained by interchanging the role of
the perturbation and the unperturbed system. The existence of this dual series
implies that a dual KAM theorem holds and, when a leading order Hamiltonian
exists that is non degenerate, the effect of tori reforming can be observed
with a system passing from regular motion to fully developed chaos and back to
regular motion with the reappearance of invariant tori. We apply these results
to a perturbed harmonic oscillator proving numerically the appearance of tori
reforming. Tori reforming appears as an effect limiting chaotic behavior to a
finite range of parameter space of some Hamiltonian systems. Dual KAM theorem,
as proved here, applies when the perturbation, combined with a kinetic term,
provides again an integrable system.
