Controllability of perturbed twist map

Umesh Vaidya and Igor Mezic

Abstract: 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.