We define the n-lift of a one-dimensional system . The n-lift can be thought of as a perturbation of the one-dimensional system depending on the state of the system n-1 time-steps back. We prove that certain f-invariant Cantor sets give invariant Cantor sets in the lifted system. We prove that if f has an invariant hyperbolic Cantor set then the lifted system has an invariant hyperbolic Cantor set provided the derivatives of f obey a simple condition. We also prove that hyperbolicity is preserved if the same conditions on the derivatives of f hold.