Embedding smooth diffeomorphisms in flows

In this paper we study the problem on embedding germs of smooth diffeomorphisms in flows in higher dimensional spaces. First we prove the existence of embedding vector fields for a local diffeomorphism with its nonlinear term a resonant polynomial. Then using this result and the normal form theory, we obtain a class of local C-k diffeomorphisms for k is an element of N boolean OR {infinity, omega} which admit embedding vector fields with some smoothness. Finally we prove that for any k is an element of N boolean OR {infinity} under the coefficient topology the Subset of local C-k diffeomorphisms having an embedding vector field with sonic smoothness is dense in the set of all local C-k diffeomorphisms. (C) 2009 Elsevier Inc. All rights reserved.