Assuming that a differential equation has a hyperbolic invariant set,
we discuss the existence of a similar invariant set for the map define
d by a numerical approximation, as well as the closeness of these sets
in the C-1-topology. Particular emphasis is given to equilibrium poin
ts, periodic orbits and invariant tori for the differential equation.
We present also a result on the preservation of structural stability f
or gradient systems. (C) Elsevier Science Inc., 1998.