The local flow-box theorem for discretizations. The analytic case

The discretization counterpart of the C-w local flow-box theorem, a C-w nor mal form result for one-step discretizations of ordinary differential equat ions in the vicinity of nonequilibria is presented. The very same problem i n the less smoother function class C-k, k less than or equal to infinity ha s been investigated in [10]. The remaining analytic case requires completel y different techniques, The proof is based on the parametrized version of a Nash-Moser type implicit function theorem by Belitskii and Tkachenko [5,6] . Connections to results on structural stability under discretization and b ackward error analysis are also investigated.