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 considered. The existence of a discretized normally hyperbolic 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 et al. [1] pproach and supplying the necessary estimates. (C) 2001 Elsevier Science Ltd. All rights reserved.
normal hyperbolicity invariant manifolds graph transformation one-step discretizations smoothness properties of composition and inversion