کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6417229 | 1338651 | 2011 | 16 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: The embedding flows of Câ hyperbolic diffeomorphisms The embedding flows of Câ hyperbolic diffeomorphisms](/preview/png/6417229.png)
In [Weigu Li, J. Llibre, Xiang Zhang, Extension of Floquet's theory to nonlinear periodic differential systems and embedding diffeomorphisms in differential flows, Amer. J. Math. 124 (2002) 107-127] we proved that for a germ of Câ hyperbolic diffeomorphisms F(x)=Ax+f(x) in (Rn,0), if A has a real logarithm with its eigenvalues weakly nonresonant, then F(x) can be embedded in a Câ autonomous differential system. Its proof was very complicated, which involved the existence of embedding periodic vector field of F(x) and the extension of the Floquet's theory to nonlinear Câ periodic differential systems. In this paper we shall provide a simple and direct proof to this last result.Next we shall show that the weakly nonresonant condition in the last result on the real logarithm of A is necessary for some Câ diffeomorphisms F(x)=Ax+f(x) to have Câ embedding flows.Finally we shall prove that a germ of Câ hyperbolic diffeomorphisms F(x)=Ax+f(x) with f(x)=O(|x|2) in (R2,0) has a Câ embedding flow if and only if either A has no negative eigenvalues or A has two equal negative eigenvalues and it can be diagonalizable.
Journal: Journal of Differential Equations - Volume 250, Issue 5, 1 March 2011, Pages 2283-2298