A symplectic twist map near an anti-integrable limit has an invariant set t
hat is conjugate to a full shift on a set of symbols. We couple such a syst
em to another twist map in such a way that the resulting system is symplect
ic. At the anti-integrable limit we construct a set of nonzero measure of o
rbits of the second map that drifts arbitrarily far, even when the coupling
is arbitrarily small. Moreover, these drifting orbits persist near the ant
i-integrable limit. (C) 2001 Published by Elsevier Science B.V.