The local flow-box theorem for discretizations the analytic case

The discretization counterpart of the C^w local flow-box theorem, a C^w normal form result for one-step discretizations of ordinary differential equations in the vicinity of nonequilibria is presented. The very same problem in the less smoother function class c^k, k∞ has been investigated in lo]. The remaining analytic case requires completely 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 discrctization and backward error analysis are also investigated.