Embedding smooth diffeomorphisms in flows |
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Authors: | Xiang Zhang |
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Affiliation: | Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, People's Republic of China |
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Abstract: | 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 Ck diffeomorphisms for k∈N∪{∞,ω} which admit embedding vector fields with some smoothness. Finally we prove that for any k∈N∪{∞} under the coefficient topology the subset of local Ck diffeomorphisms having an embedding vector field with some smoothness is dense in the set of all local Ck diffeomorphisms. |
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Keywords: | 34A34 34C41 37G05 58D05 |
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