Controllability of perturbed twist map
Umesh Vaidya and Igor Mezic
In this paper we have shown that for the two dimensional perturbed twist
map which satisfy the intersection property (i.e. any curve in the phase
space intersect its image curve) no invariant structure will survive if
the perturbation is made function of time.
Using result from ergodic theory we have shown that global controllability
can be obtained using arbitrary small time dependent perturbation.