Embedding smooth diffeomorphisms in flows

作者：Zhang, Xiang^*

来源：Journal of Differential Equations, 2010, 248(7): 1603-1616.

DOI：10.1016/j.jde.2009.09.013

• Local diffeomorphism
• Embedding flow
• Smoothness

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.

• 出版日期2010-4-1
• 单位上海交通大学