Estimates in discretizing normally hyperbolic compact invariant manifolds of ordinary differential equations

Discretization methods in the vicinity of normally hyperbolic compact invariant manifolds of ordinary differential equations are consisered. The existence of a discretized normally hyperboic compact invariant manifold is proved and, in various metric topologies, the distance between the original manifold and its discretized counterpart is estimated. Proofs are based on reconsidering the Hirsch [1] approach and supplying the necessary estimates.